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7212019 A Computational Atlas of the Hippocampal Formation Using Ex Vivo Ultra-high Resolution MRI- Application to Adahellip

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A computational atlas of the hippocampal formation using ex vivoultra-high resolution MRI Application to adaptive segmentation of in vivo MRI

Juan Eugenio Iglesias ab Jean C Augustinack b Khoa Nguyen b Christopher M Player b Allison Player bMichelle Wright b Nicole Roy b Matthew P Frosch c Ann C McKee def g Lawrence L Wald b Bruce Fischl bhKoen Van Leemput bi jk for the Alzheimers Disease Neuroimaging Initiative 1

a Basque Center on Cognition Brain and Language San Sebastiaacuten Spainb Martinos Center for Biomedical Imaging Massachusetts General Hospital Harvard Medical School Boston MA USAc CS Kubik Laboratory for Neuropathology Pathology Service Massachusetts General Hospital Harvard Medical School Boston MA USAd Department of Neurology Boston University School of Medicine Boston MA USAe Department of Pathology Boston University School of Medicine Boston MA USAf United States Department of Veterans Affairs VA Boston Healthcare System Boston MA USAg Bedford Veterans Administration Medical Center Bedford MA USAh Computer Science and AI lab Massachusetts Institute of Technology Cambridge MA USAi Department of Applied Mathematics and Computer Science Technical University of Denmark Denmark

j Department of Information and Computer Science Aalto University Finlandk Department of Biomedical Engineering and Computational Science Aalto University Finland

a b s t r a c ta r t i c l e i n f o

Article history

Received 5 July 2014

Accepted 20 April 2015

Available online 29 April 2015

Automated analysis of MRI data of the subregions of the hippocampus requires computational atlases built at

a higher resolution than those that are typically used in current neuroimaging studies Here we describe the

construction of a statisticalatlas of the hippocampalformation at the subregion level using ultra-high resolution

ex vivo MRI Fifteen autopsy samples were scanned at 013 mm isotropic resolution (on average) using custom-

ized hardware The images were manually segmented into 13 different hippocampal substructures using a pro-tocol speci1047297cally designed forthis study precisedelineations weremade possibleby theextraordinaryresolution

of the scans In addition to thesubregions manual annotationsfor neighboring structures (eg amygdala cortex)

were obtained from a separate dataset of in vivo T1-weighted MRI scans of the whole brain (1 mm resolution)

The manual labels from the in vivo and ex vivo data were combined into a single computational atlas of the

hippocampal formation with a novel atlas building algorithm based on Bayesian inference The resulting atlas

can be used to automatically segment the hippocampal subregions in structural MRI images using an algorithm

that can analyze multimodal data and adapt to variations in MRI contrast due to differences in acquisition hard-

ware or pulse sequences The applicability of the atlas whichwe arereleasing as part ofFreeSurfer (version 60)

is demonstrated with experiments on three different publicly available datasets with different types of MRI

contrast Theresultsshowthat theatlasand companion segmentation method1) cansegmentT1 andT2 images

as well as their combination 2) replicate 1047297ndings on mild cognitive impairment based on high-resolution T2

data and 3) can discriminate between Alzheimers disease subjects and elderly controls with 88 accuracy in

standard resolution(1 mm)T1 data signi1047297cantly outperformingthe atlas in FreeSurfer version53 (86accuracy)

and classi1047297cation based on whole hippocampal volume (82 accuracy)

copy 2015 The Authors Published by Elsevier Inc This is an open access article under the CC BY-NC-ND license(httpcreativecommonsorglicensesby-nc-nd40 )

NeuroImage 115 (2015) 117ndash137

Corresponding author at Basque Center on Cognition Brain and Language San Sebastiaacuten Spain

E-mail address eiglesiasbcbleu (JE Iglesias)1 Data usedin preparationof this articlewere obtained from the AlzheimersDiseaseNeuroimaging Initiative (ADNI) database (adniloniuscedu) As such theinvestigators within the

ADNIcontributed to the design and implementation of ADNI andor provideddata butdid not participate in analysis or writingof thisreport A completelisting of ADNIinvestigators can

be found at adniloniusceduwp-contentuploadshow_to_applyADNI_Acknowledgement_Listpdf

httpdxdoiorg101016jneuroimage201504042

1053-8119copy 2015 The Authors Published by Elsevier Inc This is an open access article under the CC BY-NC-ND license (httpcreativecommonsorglicensesby-nc-nd40 )

Contents lists available at ScienceDirect

NeuroImage

j o u r n a l h o m e p a g e w w w e l s e v i e r c o m l o c a t e y n i m g



Introduction

The hippocampal formation is a brain region with a critical role in

declarative and episodic memory (Scoville and Milner 1957 Eldridge

et al 2000) as well as a focus of structural change in normal aging

(Petersen et al 2000 Frisoni et al 2008) and diseases such as epilepsy

(Cendes et al 1993) and most notably Alzheimers disease (AD)

(Laakso et al 1998 Du et al 2001 Apostolova et al 2006) The hippo-

campal formation consists of a number of distinct interacting subre-gions which comprise a complex heterogeneous structure Despite its

internal complexity limits in MRI resolution have traditionally forced

researchers to model the hippocampus as a single homogeneous struc-

ture in neuroimaging studies of aging and AD (Boccardi et al 2011

Chupin et al 2009) Even though these studies have shown that

whole hippocampal volumes derived from automatically or manually

segmented MRI scans are powerful biomarkers for AD ( Convit et al

1997 Jack et al 1999 Frisoni et al 1999 De Toleto-Morrell et al

2000 den Heijer et al 2006 Wang et al 2003 Fischl et al 2002 )

treating the hippocampus as a single entity disregards potentially useful

information about its subregions In animal studies these subregions

have been shown to have different memory functions ( Acsaacutedy and

Kaacuteli 2007 Hunsaker et al 2008 Kesner 2007 Rolls 2010 Schmidt

et al 2012) In humans they are also thought to play different roles in

memory and learning (Gabrieli et al 1997 Acsaacutedy and Kaacuteli 2007

Knierim et al 2006 Kesner 2013 Kesner 2007 Reagh et al 2014

Yassa and Stark 2011) and to be affected differently by AD and normal

aging mdash as indicated by ex vivo histological studies (Braak and Braak

1991 Braak and Braak 1997 Arnold et al 1991 Thal et al 2000

Brady and Mufson 1991 Simic et al 1997 Harding et al 1998)

Findings from histological studies on hippocampal samples have

sparked interest in studying the hippocampal subregions in vivo with

MRI which has been made possible by recent advances in MRI acquisi-

tion Neuroimaging studies that have characterized the subregions in

normal aging and AD with in vivo MRI include (Mueller et al 2007

Wang et al 2009 Mueller et al 2010 Small et al 2011 Kerchner

et al 2012 Wisse et al 2012 2014 Burggren et al 2008) Most of

these studies rely on manual segmentations made on T2-weighted MRI

data of thehippocampalformation TheT2 imagesare often acquiredan-isotropically such that resolution along the direction of the major axis of

the hippocampus is reduced in exchange for higher in-plane resolution

within each coronal slice This design choice is motivated by the internal

structure of the hippocampus resembling a Swiss roll its spiral structure

changes less rapidly along its major axis which is almost parallel to the

anteriorndashposterior direction In in vivo T2-weighted data part of this spi-

ral becomes visible as a hypointense band that corresponds to the stra-

tum radiatum lacunosum moleculare hippocampal sulcus and

molecular layer of the dentate gyrus These layers separate the hippo-

campus from the dentate gyrus Henceforth for simplicity in writing

we will refer to this band as the ldquomolecular layerrdquo2

Manual segmentation protocols of high resolution in vivo MRI data

of the hippocampal sub1047297elds3 often rely heavily on this molecular

layer which is the most prominent feature of the internal region of the hippocampus that is visible in MRI However manual delineation

of the subregions in these high-resolution images is extremely labor-

intensivemdash approximately 50 hoursper caseFew laboratories currently

possess the resources in neuroanatomical expertise and staf 1047297ng that

are required to carry out such studies Even within those laboratories

the number of cases that can be used in a study is limited by how

time-consuming manually tracing the subregions is which in turns

limits the statistical power of the analysis

These limitations can be overcome with the use of automated

algorithms Two major methods have been proposed for automated

and semi-automated hippocampal subregion segmentation so far In

(Yushkevich et al 2010) ndash further validated in (Pluta et al 2012) ndash

Yushkevich and colleagues combined multi-atlas segmentation similarity-

weighted voting and a learning-based label bias correction technique to

estimate the subregion segmentation in a nearly automated fashionThe user needed to provide an initial partitioning of MRI slices into hip-

pocampal head body and tail (this requirement was dropped in their

recent study Yushkevich et al 2015) In (Van Leemput et al 2009)

our group introduced a fully automated method based on a statistical

atlas of hippocampal anatomy and a generative model of MRI data

These two methods approach the segmentation problem from dif-

ferent perspectives mdash parametric and non-parametric The algorithm

we developed ndash which follows a generative parametric approach ndash

focuses on modeling the spatial distribution of the hippocampal

subregions and surrounding brain structures (ie the underlying

segmentation) which is learned from labeled training data The seg-

mentation which is a hidden variable in the model is connected to

the observed image data through a generative process of image formation

that does notmake any assumptionsabouttheMRI acquisitionThisisindeed

the strongest point of the algorithm since it makes it adaptive to any MRI

pulse sequence and resolution that might have been used to acquire the

datamdasheven if multimodal (Puontiet al 2013) Converselythealgorithmde-

veloped by Yushkevich and co-workers relies on a combination of a

registration-based multi-atlas algorithm (a non-parametric method) and

machine learning techniques Both components of their method effectively

exploit prior knowledge about the distribution of image intensities derived

from training data mdash information which our parametric method disregards

Whilethe useof priorknowledgeaboutthe image intensitiesis advantageous

when the MRI pulse sequence of the test scan matches that of the training

data segmentation of MRI images with different contrast properties is not

possible with such an approach Nonetheless both Yushkevichs method

and ours have successfully been used to carry out subregion studies on

large populations (Teicher et al 2012 Das et al 2012 Iglesias et al 2013)

Our original sub1047297eld segmentation method which is publicly availableas part of the FreeSurfer open-source software package (Fischl FreeSurfer

2012) (version 53) is based on a probabilistic atlas that was built from

in vivo MRI data acquired at 038 times 038 times 08 mm resolution (Van

Leemput et al 2009) Henceforth we refer to this atlas as the ldquoin vivo

atlasrdquo (FreeSurfer v53) The resolution of this atlas is only suf 1047297cient to pro-

duce a coarse segmentation of the subregions in standard-resolution MRI

(ie 1 mm) a more accurate model of anatomy is necessary to analyze

newer higher resolution data where the hippocampal substructures are

more clearly visualized Speci1047297cally the in vivo atlas in FreeSurfer v53 suf-

fersfromthree shortcomings First the image resolution of the in vivo train-

ing data was insuf 1047297cient for the human labelers to completely distinguish

the subregions forcing them to heavily rely on geometric criteria to trace

boundaries which affected the accuracy of their annotations In particular

a problematic consequence is that the molecular layer was not labeledcompromising the ability of the atlas to segment high-resolution in vivo

data A second issue is that the delineation protocol was designed for the

hippocampal body and did not translate well to the hippocampal head or

tail Due to the second issue a third problem is that the volumes of the sub-

regions did not agreewell with those from histological studies (Simic et al

1997 Harding et al 1998) as pointed out by (Schoene-Bake et al 2014)

In this studywe address these shortcomings by replacingthe hippo-

campal atlas in FreeSurfer v53 with a new version (FreeSurfer v60)

built with a novel atlasing algorithm and ex vivo MRI data from autopsy

brains Since motion effects are eliminated much longer MRI acquisi-

tions are possible when imaging post-mortem samples Our ex vivo

imaging protocol yields images with extremely high resolution and

signal-to-noise ratio dramatically higher than is possible in vivo

which allows us to accurately identify more subregions with a

2 This band hasbeen referred to as theldquodarkbandrdquo in theliteraturebut is actually bright

when imaged with T1-weighted MRI therefore we prefer to use the term ldquomolecular

layerrdquo3 We use the term ldquosub1047297eldsrdquo to refer to the CA structures (ie CA1ndash4) and subregions

to refer to the whole set of hippocampal substructures including parasubiculum

presubiculumsubiculum1047297mbriamolecularlayer and hippocampusndashamygdala transition

area (in addition to the sub1047297elds)

118 JE Iglesias et al NeuroImage 115 (2015) 117 ndash137



delineation protocol speci1047297cally designed for this study To the best of

our knowledge there is only one ex vivo atlas of the hippocampus pre-

sented in Yushkevich et al (2009) Adler et al (2014) have presented

promising work towards an atlas based on both ex vivo MRI and histol-

ogy but they only labeled one case Compared with Yushkevichs atlas

(henceforth ldquoUPenn atlasrdquo) the ex vivo atlas (FreeSurfer v60) has the

following advantages 1 it is built at a higher resolution (013 mm iso-

tropic on average vs 02 mm) 2 it models a larger number of struc-

tures (15 vs 5) 3 it is built upon a larger number of cases (15 vs 5)and4 in addition to the hippocampal subregions it also modelsthe sur-

rounding structures which enables its use in a generative modeling

framework to directly segment in vivo MRI data of varying contrast

properties To include the neighboring structures in the atlas we

have developed a novel atlas construction algorithm that combines

the dedicated ex vivo data with a standard resolution dataset of

in vivo scans of the whole brain for which manual labels of the sur-

rounding tissue are already available this algorithm eliminates the

need to delineate the neighboring structures at ultra-high resolu-

tion which would be extremely time consuming Throughout this

article we will refer to the hippocampal atlas resulting from these

delineations as the ldquoex vivo atlasrdquo (FreeSurfer v60) mdash even though

as explained above in vivo data were used to include the structures

around the hippocampus in the model

In addition to theatlaswe also present in this study a segmentationalgo-

rithm for analyzing in vivo MRI scans with the ex vivo atlas The method is

largely based on (Van Leemput et al 2009) It is important to stress that a

procedure that can adapt to different intensity distributions is required for

using ex vivo data to infer in vivo structures The ex vivo scans are acquired

on1047297xed tissue withdramatically different contrastproperties than in vivo tis-

sue The1047297xation process cross-links proteins signi1047297cantly shortening T1 and

leaving little remaining T1-contrast As a result the ex vivo scans that we ac-

quire are largely T2 weighted Thus even if one was to match acquisition

protocols in vivo and ex vivo the resulting images would have dramatically

different intensity characteristics due to the changes in the intrinsic tissue

properties that give rise to MRI contrast Therefore to take advantage of the

ultra-high resolution images that can only be obtained ex vivo one must

use a procedure that does not require the same intensity characteristics in

the atlas as in the in vivo scans to be segmentedThe rest of the paper is organized as follows Section Atlas construction

describes the MRI data delineation protocol and mathematical framework

that were used to build the statistical atlas shows the resulting atlas and

compares the subregion volumes that it yields with those from the UPenn

atlas and from two histological studies Segmentation of in vivo MRI data

details an algorithm to use the atlas to segment in vivo MRI data and pre-

sents results on three datasets with different resolutions and types of MRI

contrast Finally Discussion and Conclusion concludes the article

Atlas construction

The statistical atlas that we propose is built from a combinationof

ex vivo and in vivo MRItraining data Here we1047297rst describethe acqui-

sition (Autopsy brain samples and ex vivo MRI acquisition) andmanual labeling (Manual segmentation of ex vivo MRI data ana-

tomical de1047297nitions) of the ex vivo data Next we introduce the

in vivo training data we used (In vivo training MRI data) The algo-

rithm to build the atlas is described in Algorithm for atlas

construction and the resulting atlas presented in Statistical atlas

volumes of subregions and sample slices

Autopsy brain samples and ex vivo MRI acquisition

The ex vivo data consists of 1047297fteenautopsied brainhemispheres from

two different sources Eight of the samples were from the Framingham

Heart Study and Boston University Alzheimers Disease Center

(Veterans Administration Medical Center Bedford VA) The other

seven samples were from the Massachusetts General Hospital Autopsy

Service (Massachusetts General Hospital Boston MA) The samples

consisted of whole brain hemispheres (left n = 8 right n = 7) from

15 different subjects Ten of the subjects did not have any neurological

conditions whereas four of them had mild AD and one had mild cogni-

tive impairment (MCI) Eight samples were 1047297xed with periodatendash

lysinendashparaformaldehyde (PLP) and the other seven were 1047297xed

with 10 formalin The demographics of the ex vivo samples were the

following age at death was 786 plusmn 119 years 357 were females

533 were left hemispheres and the post-mortem interval was lessthan 24 h in all cases for which this information was available The

demographics are detailed in Table 1

A block of tissue including the hippocampus was excised from each

ex vivo sample Depending on its size the block was placed in either a

plastic cylindrical centrifuge tube (60 ml 3 cm diameter) or if it did

not 1047297t inside a bag 1047297lled with PLP and sealed In the latter case air

was pumped out using a needle and a vacuum pump in order to mini-

mize the number and size of air bubbles in the samples Two different

pumps were used in the process a DV-185 N-250 Platinum 10 CFM

by JB (Aurora IL) and a S413801 by Fisher Scienti1047297c (Hampton NH)

The tissue block was subsequently scanned in a 7 T Siemens scanner

using a 3D FLASH sequence with TR = 50 msec TE = 25 msec α = 20deg

Two of the samples were scanned at 01 mm isotropic resolution seven

at 012 mm 1047297ve at 015 mm and one at 02 mm (see Table 1) Three dif-

ferent coils were used in the acquisition accommodating variations in

sample size a 4-turn solenoid coil (285 mm inner diameter 44 mm

length) a 4-channel phased-array (a linear array of loop coil elements

each with 5 cm coil diameter 15cm overlap between adjacentelements

16 cm in length) and a small birdcage (24 rings outer diameter =

197 cm inner diameter = 193 cm length = 12 cm) Despite the fact

that different coils were used to scan the different samples the output

images were comparable in quality The whole procedure received IRB

approval before its execution by the Partners Human Research Commit-

tee Fig 1 displays some sample slices of the data

Manual segmentation of ex vivo MRI data anatomical de 1047297nitions

In this section we describe the protocol for manually labeling thehippocampal subregions in the ex vivo data Theprotocol was speci1047297cal-

ly designed forthis study andis largely based on thehistology and mor-

phometry from (Rosene and Van Hoesen 1987) and partly also on

(Lorente de No 1934 Insausti and Amaral 2011 Green and Mesulam

1988) The Duvernoy atlas (Duvernoy 1988) was also used as an aid

in the delineation process The set of annotated labels along with the

protocol for their annotation is described in Table 2 The descriptions

in the table are based on ex vivo contrast not histological data Given

the excellent resolution of the ex vivo MRI data (100 μ m) most of the

Table 1

Demographics of the subjects whose hippocampi were used in this study PMI stands for

post-morteminterval The resolution was isotropic in all casesNA represents unavailabil-

ity of that demographic datum for that subject

Cas e Ag e Gender Laterality Re solution Diagnosis P MI

1 NA Male Left 100 μ m AD NA

2 NA Female Left 120 μ m AD 21 h

3 91 Female Right 120 μ m Control 16 h

4 83 Female Left 150 μ m AD 55 h

5 89 Female Right 120 μ m AD NA

6 82 Male Right 120 μ m Control NA

7 63 Male Left 120 μ m Control NA

8 87 Male Left 120 μ m MCI 21 h

9 67 Male Right 150 μ m Control 12 h

10 NA Male Left 150 μ m Control 65 h

11 NA Male Right 150 μ m Control NA

12 NA Male Left 150 μ m Control NA

13 60 Male Right 120 μ m Control b24 h

14 86 Female Left 100 μ m Control 12ndash24 h

15 NA NA Right 200 μ m Control NA




subregion boundaries were visible in the images but subtle transitions

were still dif 1047297cult to distinguish Another source of differences between

our ex vivo MRIlabels and histology is that many boundaries are oblique

(rather than perpendicular) to the imaging planes Nonetheless

we used previously published anatomical contrast to guide us

(Augustinack et al 2005 Fischl et al 2009 Augustinack et al 2010

Augustinack et al 2013) We also used neuroanatomical knowledge of

particular layers to help us identify boundaries

Distinguishing the boundaries between subiculum CA1 CA2 and

CA3 was more dif 1047297cult due to the lack of image contrast betweenthose sub1047297elds but we used the pyramidal layer thickness and pyra-

midal layer intensity for this We also combined the knowledge of

location and pyramidal layer thickness to determine the subregions

the subiculum is widest CA1 is thinner than subiculum CA2 is thinner

than CA1 and 1047297nally CA3 is the thinnest of the sub1047297elds To distin-

guish the subicular boundaries we used neighboring neuronal group-

ings such as entorhinal layer II islands (Augustinack et al 2005)

presubicular clouds (Green and Mesulam 1988) and reduced lamina-

tion in parasubiculum (compared with presubiculum and entorhinal

cortex Green and Mesulam 1988) A full descriptionof the histologic ar-

chitecture is beyond the scope of this work because the atlas described

here is based on ex vivo contrast Nonetheless our ex vivo MRI delinea-

tions represent a signi1047297cant improvement over the previous FreeSurfer

hippocampal segmentation (that only used geometric properties) andare much closer to the underlying subregion boundaries

Seven manual labelers that were supervised by JCA used the proto-

col described in Table 2 to annotate the subregions in the 15 ex vivo

scans Annotating each scan took approximately 60 h a single hippo-

campus at this resolution contains more voxels than an in vivo scan of

an entire brain The annotations were made using Freeview a visualiza-

tion tool that is included in FreeSurfer The1047297rst step in the protocol was

to rotate the MRI volume to align the major axis of the hippocampus

with the perpendicular direction to the coronal view Then assuming

a left hippocampus (in right hemispheres the image was 1047298ipped

for delineation) the subregions were labeled using the de1047297nitions in

Table 2 When bubbles were present in the images the labelers 1047297lled

them with the label of the structure they believe would be under the

bubble Since this introduces noise in the manual labels minimizing

the number and size of air bubbles in the sample prior to acquisition

was crucial The delineations were made in coronal view while using

information from the other two views (sagittal and axial) to guide the

tracing even though this might lead to slightly jagged boundaries in

sagittal and axial view this roughness is averaged out when the manual

segmentations are downsampled and combined into the probabilistic

atlas (see Statistical atlas volumes of subregions and sample slices )

In order to ensure the consistency between the manual labelers JEI

and JCA evaluated their delineations and served as quality control

for each case re1047297ning the segmentations where necessary Samplemanual tracings along with the color coding of the subregions (for

visualization purposes) are shown in Fig 2

In vivo training MRI data

Learning the spatial distribution of labels surrounding the hippocam-

pus from the ex vivo data requires manual delineation of its neighboring

structures Even though it would be possible to trace these structures on

ultra-high resolution ex vivo MRI data such approach would represent

an unnecessary labeling effort for two reasons First the neighboring

structures only need to provide a course context to assist the segmenta-

tion of the hippocampal subregions and therefore do not require labeling

at ultra-high resolution which is extremely time consuming delinea-

tion at standard resolution (ie ~1 mm) is suf 1047297cient And secondthere is already a number of publicly available and proprietary in vivo

datasets for which such structures have already been manually labeled

These are the motivations for using an additional training dataset

consisting of in vivo whole brain MRI scans The dataset consists of

T1-weighted scans from 39 subjects (19 males 20 females mean age

563 years 29 controls 10 mildly demented) acquired with a MP-

RAGE sequence in a 15 T scanner with the following parameters

TR = 97 ms TE = 4ms TI = 20 ms 1047298ip angle = 10deg 1 mm isotropic

resolution Thirty-six brain structures including the whole left and

right hippocampi were manually delineated using the protocol de-

scribed in (Caviness et al 1989) see sample slices as well as a qualita-

tivecomparison with the ex vivo delineationprotocol in Fig3 Note that

these are the same subjects that are used to construct the probabilistic

atlas in FreeSurfer

Fig 1 Sample sagittal (a)coronal (b)and axial (c)slicesfrom the ex vivo dataof Case8 Sample sagittal(d) coronal(e) andaxial (f)slicesfrom theex vivoMRIdata ofCase14In (e) two regions

of the slice are zoomed in to better appreciate thelevelof resolution of thescan (01 mm) Note that theacquisition of Case 8 was carried outin a bag whereas Case 14 was scanned in a tube




Algorithm for atlas construction

Here we describe the procedure to build the probabilistic atlas

from in vivo and ex vivo data We will 1047297rst describe the underlying

model which is based on a tetrahedral mesh representation Then we

will useBayesian inferenceto learntheparameters of themesh from man-

ualannotations assuming that itstopology is1047297xed Finally we introducea

Bayesian algorithmto optimize thetopology of themeshwhichis a model

selectionproblem Throughout therest of this section we will assumethat

allthetraining samples correspond to left hippocampi samples from right

hippocampi are simply 1047298ipped before being fed to the algorithm

Underlying model

To build the probabilistic atlas of the hippocampal formation from

ex vivo and in vivo data we developed a generalization of our previous

method (Van Leemput et al 2009) that can deal with partial

Table 2

Protocol for manual segmentation of the ex vivo MRI data

Structure De1047297nition

Alveus (beige) The alveus a white matter structure covers the hippocampus on the superior rim It is the white matter directly adjacent to the cornu ammonis not

extending separately (such as 1047297mbria) The alveus borders the amygdala at the anterior end and fuses with the 1047297mbriafornix at the posterior end The

alveus extends from the 1047298oor of the inferior horn of the lateral ventricle until it meets the cerebral white matter where the ventricle ends laterally The

alveus is present throughout the rostrocaudal regions of the hippocampus (head body and tail) The alveus appears dark in FLASH MRI

Parasubiculum

(yellow)

The parasubiculum is Brodmanns area 49 Parasubiculum is considered periallocortex (~5 ndash6 layers) and lies on the lower bank of the hippocampal

1047297ssure Parasubiculum is the medial-most of the subicular cortices with presubiculum laterally and entorhinal cortex medially The parasubiculum isrelatively small compared to the subiculum and presubiculum Parasubiculum displays less lamination than presubiculum and entorhinal cortex in

ex vivo MRI (ie super1047297cial layers about the same size thickness and contrast as infragranular layers)

Presubiculum

(dark purple)

The presubiculum is Brodmanns area 27 The presubiculum is periallocortex and has distinct super 1047297cial layers with a heavily myelinated molecular

layer The presubiculum makes up a large portion of territory on the lower bank of the hippocampal 1047297ssure in the human brain and extends posteriorly

to the retrosplenial region The presubiculum lies between the parasubiculum (medially) and the subiculum (laterally) The contrast in presubiculum is

heterogeneous with light and dark contrast in its super1047297cial layer(the lamina principalisexterna) making it a particularly distinctive pattern in ex vivo

MRI The lamina principalis externa of the presubiculum ends at the subiculum

Subiculum (blue) The subiculum belongs to the allocortex group mdash three layered cortex with a molecular layer a pyramidal layer and a polymorphic layer As the light

and dark contrast of the presubiculum ends the subiculum begins laterally The boundary between presubiculum and subiculum is distinct because the

subiculum has a well-de1047297ned pyramidal layer in ex vivo MRI The pyramidal layer in the subiculum widens (compared to presubiculum) and ramps up

from a narrow wedge to full-1047298edged allocortex The molecular layer appears directly superior to the subiculum It is between presubiculum and

subiculum that the cortex simpli1047297es to a three-layered cortex We did not segment the prosubiculum

CA1 (red) The subiculum transitions into CA1 laterally CA1 displays light homogeneous contrast for the pyramidal layer similar to the subiculum and other CA

1047297

elds The subiculumCA1 boundary occurs approximately where the hippocampus turns upward (at 7 oclock using the letter C as a representation forthe hippocampus and radiologic convention for the right side) We labeled the hippocampal molecular layer separately from CA1 pyramidal layer

because we could distinguish the difference CA1 continues until the top of the 1047297rst hippocampal fold where it meets CA2 CA1 dominates at the

hippocampal head and lessens in the hippocampal body The uncal (medial) portion of CA1 was included in the CA1 label

C A2 3 ( gr een) W e c om bined sub1047297elds CA2 and CA3 due to lack of distinguishing contrast in MRI and variability among our labelers in preliminary experiments We

encountered great variability particularly with the angle of the original CA2 label CA23 showed a light intensity and homogeneous contrast as the

pyramidal layer in CA1 but the pyramidal layer of CA23 appeared thinner than in CA1 The thickness change between CA1 and CA23 was a

distinguishing feature to delineate these two sub1047297elds When this change was gradual the boundary was placed approximately in the center of the

region of varying thickness CA23 extended from the posterior half of the hippocampal head to the tail CA23 was typically superior to the dentate

gyrus but also weaved throughout hippocampal folds Here we also labeled the molecular layer in CA23 separately from the CA23 pyramidal layer

CA4 (light brown) CA4 is also known as the hilar region of the dentate gyrus Topographically the CA4 sub1047297eld lies within the dentate gyrus Thus CA4 1047297lls the interior of

the GCndashDG label The limit between CA23 and CA4 is at the entrance of the hilus The contrast of CA4 has a similar contrast to CA1ndash3 but lighter

contrast for the polymorphic layer Thus in ex vivo MRI with a FLASH sequence it appears slightly darker intensity in the inner-most portion (ie the

modi1047297ed pyramidal area of CA4) but lighter outside of that (ie the polymorphic cell layer of the dentate gyrus) The ability to distinguish these

particular strata depended on the brain quality and resolution We included the polymorphic layer in our CA4 label

GCndashDG granule celllayer of dentate

gyrus (cyan)

The dentate gyrus is another three layered structure The dentate gyrus consists of a molecular layer a granule cell layer and a polymorphic layer Thegranule cell layer shows abright white intensity with a FLASH sequence in ex vivo MRI the intense contrast likely due to the high packing density of the

granule cells The molecular layer of the dentate gyrus has dark contrast and was included in the CA4 label because we could not always distinguish the

stratum The dentate gyrus begins about one third to halfway through the hippocampal head from the rostral-most slices The shape of the dentate

gyrus varies depending on the cut plane

HATA (light green) The hippocampusndashamygdala-transition-area (HATA) lies in the medial region of the hippocampus and is superior to the other sub1047297elds The HATA

shows a dark intensity compared to the CA sub1047297elds Its base forms the medial and slightly dorsal border of the hippocampus but this may depend on

orientation We consistently observed that the top of the hippocampal folds (ie the superior-most folds) were a tangential landmark to delineate the

HATA inferior boundary The inferior horn of the lateral ventricle borders the medial side of the HATA and the alveus borders the HATA laterally

Fimb ria ( violet ) The1047297mbria is a white matter structure that extends from the alveus and eventually forms the fornix The 1047297mbria exits posteriorly the mid-body level of

the hippocampus and has the same dark intensity as the alveus

Molecular layer

(brown)

This label consists of two parts molecular layer for subiculum or molecular layer for CA 1047297elds The molecular layer appears as dark contrast that lies

directly underneath the hippocampal 1047297ssure and above the subiculum The molecular layer of the hippocampus continues as dark contrast that forms

between the CA regions and the GCndashDG as well as the hippocampal 1047297ssure The molecular layer follows the shape of the hippocampal folds

Hippocampal 1047297ssure(purple)

The hippocampal 1047297ssure opens up medially and extends laterally until it is a vestigial space between the molecular layers of the hippocampus anddentate gyrus In ex vivo MRI our scanning liquid (paraformaldehyde solution) 1047297lls the ventricle as cerebrospinal 1047298uid would in the living brain Air

bubbles frequently appear as artifacts in this kind of imaging

Tail (bright green) The hippocampal tail has not been extensively studied in the neuroanatomical literature yet so it is dif 1047297cult to make reliable annotations in this region

Instead we identi1047297ed the 1047297rst coronal slice (anterior to posterior) where the fornix is fully connected to the hippocampus and labeled the whole

hippocampus with this ldquoumbrellardquo label in the remaining slices (approximately 40)




Fig 2 Eight coronal slices from Case 14 and corresponding manual annotations The slices are ordered from anterior to posterior Sagittal and axial slices as wellas 3D renderings of the

manual segmentation are shown in the supplementary material (Fig 15 Fig 16 and Fig 17)

Fig 3 In vivo dataset and comparison with ex vivo images (a) Sagittal slice in vivo (b) Corresponding manual delineation of brain structures note that the hippocampus (in yellow) is

labeled as a single entity (c) Coronal slice in vivo (d) Corresponding manual delineation e) Close-up of the hippocampus (in yellow) on a sagittal slice in vivo f) An approximately cor-

responding slice from Case 12 of the ex vivo dataset (g) Close-up of the hippocampus on a coronal slice in vivo (h) An approximately corresponding slice from Case 12 (ex vivo)




information The algorithm aims to produce a compact tetrahedralmesh representation of the atlas in which each vertex has an associated

vector of probabilities for the different hippocampal subregionsand sur-

rounding structures The topology and resolution of the mesh are locally

adaptive to the shape of each anatomical region ie coarse in uniform re-

gions and1047297ne around convolutedareasThe difference with respect to the

original method is that we nolongerassumethatall the labels of the train-

ing dataset are readily available for the ex vivo data the labels for the

surrounding structures are not given and for the in vivo data the hippo-

campal subregions are not available Instead we observe a modi1047297ed ver-

sion in which some sets of labels have been collapsed into more general

labels in a deterministic fashion (Iglesias et al 2015) The function that

collapses the labels is different for each training dataset for the ex vivo

samples it collapses all the non-hippocampal structures into a single ge-

neric background label For the in vivo data the function collapses all thehippocampal subregions into a single label corresponding to the whole

hippocampus

Speci1047297cally let there be M label volumes Cm m =12 hellip M derived

from in vivo or ex vivo data Each label volume Cm = cim i = 1 2 hellip I

has I voxels where each voxel has a manual label belonging to one of

P possible collapsed classes cimisin 1 2 hellip P We model these label im-

ages as having been generated by the following process (illustrated in

Fig 4)

a) A tetrahedral mesh covering theimage domainis de1047297ned This mesh

is described by the position of its N vertices xr = xnr n = 1 2hellip N

and their connectivity K Henceforth we will refer to xr as the refer-

ence position of the mesh Each mesh node has an assigned vector of

labelprobabilitiesαn = (α n1α n

2hellipα nL) where 1 2hellip Listhesetof

labels before collapsing The probabilities satisfyα nkge 0sumk = 1

K α nk =

1

b) M deformed meshes are obtained by sampling M times from the

following probability distribution

p xmj β xr Keth THORNprop exp minus

U xmj xr Keth THORN

β

frac14 exp minus

XT

t frac141U Kt xmj xr eth THORN

β

24

35

where xm is the deformed mesh position T is the number of tetrahe-

dra in the mesh β is a mesh 1047298exibility parameter and U Kt xj xr eth THORN is

a penalty that goes to in1047297nity if the Jacobian determinant of the tth

tetrahedrons deformation becomes zero (Ashburner et al 2000)

This deformation model allows themesh to describe a broad spectrum

of hippocampal shapes while preventing the Jacobian determinant of

the deformation of each tetrahedron from becoming zero (which isequivalent to collapsing it) or negative (which is equivalent to revers-

ing its orientation) By avoiding collapses and orientation reversals of

the tetrahedra we ensure that the topology of the mesh is preserved

Throughout the rest of this paper we will assume that β is a known

constant

c) From each deformed mesh xm a latent label lim isin 1 2 hellip L is

generated for each voxel i by sampling from the label probabilities

given by the mesh At non-vertex locations these probabilities

are computed using barycentric interpolation pi kjα xm Keth THORN frac14

sumN nfrac141α

knϕ

mn xieth THORN where pi is theprior probability at voxel i xi is the spa-

tial location of voxel i and ϕnm(sdot) is an interpolation basis function at-

tached to node n of mesh m mdash see details in (Van Leemput 2009)

Assuming conditional independence of the labels between voxels

given the deformed mesh position x

m

we have that

p L mjα xm Keth THORN frac14 prodI

ifrac141 pi lmi jα xm

K

where L m = l1m hellip lI

m is the m-th latent label volume

d) Finally the observed label volumes are given by cim = f in(li

m) (for

in vivo volumes) and cim = f ex(li

m) (for ex vivo volumes) The function

f in collapses all the hippocampal subregion labels into a single global

hippocampal label whereas f ex collapses all the non-hippocampal

labels into a singlegeneric background label Therefore we can write

pi cmi jα xm

K

frac14X

kisincmi

pi kjα xm Keth THORN eth1THORN

where kisin cim denoteslooping over the labels such that f (sdot)(li

m) = cim If

the mapping from L to C is bijective (ie no labels are collapsed) the

generative model is the same as in (Van Leemput 2009)

Given this probabilistic model the construction of the atlas is equiv-

alent to solving thefollowing inverse problem given a setof (collapsed)

label volumes (ie manual segmentations) we search for the atlas that

most likely generated them according to the model We use Bayesian

inference to 1047297nd the answer as detailed below

Optimization of model parameters mdash mesh deformations and atlas

probabilities

Assuming that the mesh connectivityK and reference position x r are

known the problem to solve is

α ^ x m g frac14 argmaxα x mf g p α x mf gj Cmf g x r Kβeth THORNn

Fig 4 Illustration of the generative model of the manual labels for ex vivo (top) and in vivo (bottom) MRI




where α and ^ x m

represent the most likely atlas probabilities and atlas

deformations respectively Using Bayes rule we have

α ^ x m

g frac14 argmaxα x mf g p Cmf gjα x mf g Keth THORN p xmf gj β xr Keth THORN frac14

n

argmaxα x mf gprodM mfrac141 p C mjα x m Keth THORN p xmj β xr

Keth THORN

where we have assumed a 1047298at prior forα ie p(α )prop 1 Now taking the

logarithm of Eq (2) and expanding the sum over voxels and hidden

labels (Eq (1)) we obtain the objective function for atlas building

fα ^ x m

g frac14 argmaxα x mf g

L α x mf g Cmf g x r β Keth THORN eth3THORN

with

L α x mf g Cmf g x r β Keth THORN

frac14XM

mfrac141

log p xmj β xr Keth THORN thorn

XI

ifrac141

logX

kisincm

i

pi kjα xm Keth THORN

8lt

9=

The1047297rst termin L inEq (3) represents the(negated) cost of warping

the mesh according to the deformation model we have borrowed from

(Ashburner et al 2000) whereas the second term represents the data

1047297delity We solve Eq (3) by optimizing α with x m 1047297xed and vice

versa until convergence Updating α amounts to re-estimating the

label probabilities at each spatial location whereas the optimization of

x m with α 1047297xed represents a group-wise nonrigid registration pro-

cess As shown below the update equations are analogous to those

from the original method (Van Leemput 2009)

Update of xm We perform the optimization of Eq (3) with respect

to xm one dataset index m at the time We use a conjugate gradient

algorithm to numerically optimize the expression The gradients are

given in analytical form by

part L α x mf g Cm x r β Keth THORN

part x m frac14 minus

1

β

XT

t frac141

part U Kt xmj xr eth THORN

part xm thorn

XI

ifrac141

XkisinC mi

part pi kjα xm Keth THORN

part xmXkisinC mi


frac14 minus1

β

XT

t frac141


part xm thorn

XI

ifrac141

XkisinC mi

XN

nfrac141α knpartϕm

n xieth THORN

part xmXkisinC mi

XN

nfrac141α knϕ

mn xieth THORN

Update of α We carry out the optimization of Eq (3) with respect

to α with an expectation maximization (EM) algorithm (Dempster

et al 1977) as follows Leaving aside the term that is independent of

α we iteratively build a lower bound to the target function L α

x

m

f gethCm x r β KTHORN that touches it a the current value of α (ldquoE steprdquo) and

subsequently optimize this bound with respect to α (ldquoM steprdquo) This

procedure is guaranteed to always improve the value of the original

target function (or leave it unchanged when convergence has been

achieved) If ~α is the current estimate of α the bound is

Q α ~α eth THORN frac14XM

mfrac141

XI

ifrac141

XN

nfrac141

Xk

W mkin log αk

nϕmn xieth THORNδ kisincm

i

h iminusW mk

in log W mkin

leXM

mfrac141

XI

ifrac141

logX

k

XN

nfrac141

α knϕmn xieth THORN δ kisincm

i

frac14XM

mfrac141

XI

ifrac141

logX

kisincm

i


where W inmk is given by the E Step

W mkin frac14

~αknϕ

mn xieth THORNδ kisincm

i

X

n0

Xk

0 ~αk0

n0ϕmn0 xieth THORNδ k

0isincmi

eth4THORN

It can easily be shown that the maximum of Q α ~α eth THORN is attained at

(M step)

αkn frac14

XM

mfrac141

XI

ifrac141W mk

inXM

m0frac141

XI

i0frac141

Xk

0 W m0k

0

i0n

eth5THORN

As mentioned previously the optimization scheme in Van Leemput

(2009) is recovered when the mapping from L to C is bijective

Optimization of mesh topology mdash model selection

So far we have assumed that the mesh connectivity and reference

position were 1047297xed Optimizing the mesh topology is important to

avoid over1047297tting to the training data due to the large variability in neu-

roanatomy across subjects For instance at a given spatial location an

atlas built upon a small training dataset could incorrectly assign a zero

probability for a given label if it was not present in any of the training

volumes This problem can be partly overcome by smoothing the atlas

(Ashburner and Friston 2001) As shown in Van Leemput (2009) the

mesh topology can be optimized such that an automatically estimated

amount of blurring is introduced in the atlas allowing it to generalize

well to previously unseen data Following Van Leemputs framework

we compare meshes with different topologies by evaluating their so-

called evidence which expresses how probable the observed training

data is for each mesh topology To compute the model evidence we fol-

low (Van Leemput 2009) with the difference that we replace

pi lmi jα xm

K

by pi cmi jα xm

K

frac14 sumkisincmi pi kjα xm

Keth THORN mdash recovering

our previous algorithm if f (middot)(l) is bijective The evidence is given by

p C mf gjβ x r Keth THORNasymp 1

Z prod

N

nfrac141N n thorn 1

N n thorn 2 h iminus1

prod

M

mfrac141 p C mjα ^ x

m K

eth6THORN

where N n frac14 sumM mfrac141sumksum

I ifrac141W mk

in α ^ xm

are the minimizers of Eq (3)

and where the constant Z includes a number of factors that only depend

signi1047297cantly on β (which is kept 1047297xed in this work)

In order to compute the most likely connectivity K and reference

position x r using Eq (6) these variables are 1047297rst initialized with a

high-resolution regular mesh Then the mesh parameters α ^ x m

are optimizedby solving the problem in Eq (3) Finallythe meshis sim-

pli1047297ed by repeatedly visiting each edge (in random order) comparing

the effect on the evidence of either keeping the edge while optimizing

the reference position of the two nodes at its ends or collapsing the

edge into a single nodeand optimizingits referenceposition the details

can be found in Van Leemput (2009)

Data preprocessing

To build the atlas all the training label volumes must be in the same

coordinate space For this purpose we carried out the following prepro-

cessing steps 1 manually rotating the FreeSurfer whole brain atlas ndash

described in (Fischl et al 2002) ndash so that the major axis of the left hip-

pocampus was aligned with the anteriorndashposterior axis 2 extracting

from the atlas a binary mask corresponding to the voxels for which

the left hippocampus is the most likely label 3 leftndashright 1047298ipping

all right hippocampi in the training data 4 af 1047297ne co-registration of

the training data (using binary hippocampal masks) to the left hippo-

campus of the rotated FreeSurfer atlas using sum of squares as metric

5 resampling to 025 mm resolution (which is above the limit that can

currently be achieved with in vivo brain MRI scanning) and 6 cropping




a bounding box around the hippocampi leaving a 10 mm margin with

respect to the boundary as de1047297ned by the FreeSurfer atlas mdash which

yielded volumes of dimension 131 times 241 times 99 voxels The resampling

of label volumes was carried out by resampling binary masks for each

label separately using cubic interpolation and picking the label with

the maximum value at each voxel This approach mitigates the block

effect caused by nearest neighbor interpolation This preprocessing

pipeline yielded 93 (78 in vivo 15 ex vivo) volumes with the same size

and resolution in which the hippocampi were af 1047297nely aligned and

which were then fed to the algorithm described above The mesh 1047298exi-

bility parameter was set to β = 015 visual inspection of the results

of pilot segmentation experiments using thealgorithmproposed in Sec-

tion Quantitative results on standard resolution ADNI T1 data below

and 10 T1 scans of the OASIS dataset4 showed that this value of β pro-

vided a good compromise between speci1047297city and generalization

ability

Statistical atlas volumes of subregions and sample slices

Coronal slices from the resulting statistical atlas are displayed in

Fig 5 The atlas has a total of 18417 vertices so the dimensionality of x ndash which is equal to the number of degrees of freedomof thenonlinear

deformation ndash is approximately three times this value ie ca 55000

4

httpwwwoasis-brainsorg

Fig 5 Correspondingcoronal slices(fromanteriorto posterior)of thelabelprobabilities derivedfromthe proposedex vivo (toptworows)and original invivo (middle tworows)atlasesas

well as the UPenn atlas (Yushkevich et al2009) (bottom two rows) For the FreeSurfer atlasesthe color at each voxel is a linearcombination of the colors assignedto the substructures

weighted by the corresponding probabilities For the UPenn atlas the color corresponds to the label with highest probability at each location The color legend for the hippocampal

subregionsis thesame asin Fig 2 Thecolor codefor the surrounding structuresis displayed in the1047297gure mdashnotethat the in vivo atlas usesgeneric labels forthe graymatter white matter

and cerebrospinal 1047298uid structures Sagittal and axial slices of the atlases are provided as part of the supplementary material (Fig 18 and Fig 19)




Fig 5 also displays the original in vivo atlas currently distributed with

FreeSurfer for comparison Both atlases show similar levels of blurring

in the label probabilities that allow them to avoid over1047297tting the train-

ing data and generalize well to test images However the ex vivo atlas

follows the internal structures of the hippocampus with much more

accuracy than the in vivo version which relies much more on geometric

featuresmdash seefor instance theverticalboundary of CA1(in red) in Fig5

In fact the in vivo atlas does not describe the molecular layer (dark

brown) which is the main feature that will allow the atlas to segment

high-resolution MRI data of the hippocampus The 1047297gure also displays

the UPenn atlas from (Yushkevich et al 2009) which has lower resolu-

tionthan the presented ex vivo atlas has fewer subregions and does not

model additional surrounding (extrahippocampal) structuresThe improved accuracy of the ex vivo atlas is also re1047298ected on the

volumes of the subregions Table 3 shows the average subregion vol-

umes for the in vivo (FreeSurfer v53) and ex vivo atlases (FreeSurfer

v60)for theUPenn atlas (Yushkevich et al 2009) and for twodifferent

previous histological studies (Simic et al 1997 Harding et al 1998)

Compared with the in vivo atlas the ex vivo counterpart models a larger

number of subregions and also yields volumes for CA1 and (especially)

CA23 that aremuch closerto those reported by thereferenced histolog-

ical studies The UPenn atlas yields accurate volumes for CA4 (for which

it agrees well with the ex vivo atlas) but underestimates the volume of

CA23 and largely overestimates the volume of CA1 Both the ex vivo

atlas and the UPenn atlas overestimate the volume of the dentate

gyrus compared with the histological studies

Segmentation of in vivo MRI data

In this section we1047297rst introduce an algorithm to segment in vivo MRI

data using the proposed statistical atlas (Algorithm for segmenting

an in vivo scan) We subsequently present segmentation results on

three different publicly available datasets with different resolutions and

MRI contrasts in order to demonstrate the ability of the algorithm to

adapt to monomodal and multimodal data acquired with different

MRI protocols and different hardware platforms In Qualitative

segmentation results on high resolution T1T2 data from Winterburn

et al (2013) the algorithm is applied to high resolution (06 mm isotro-

pic) T1T2 data segmenting the T1 and T2 channels both independently

and simultaneously In Quantitative results on ADNI T1T2 data we

use 1 mm isotropic T1 dataand corresponding high-resolution T2 images

(04 mm in-plane 2 mm slice thickness) to1047297nd group differences in sub-

region volumes between MCI subjects and elderly controls Finally in

Quantitative results on standard resolution ADNI T1 data we automati-

cally segment 1 mm isotropic T1 scans of AD subjects and elderly controls

to computevolumes that are used as feature inclassi1047297cationexperiments

Algorithm for segmenting an in vivo scan

Here we describe the algorithm to segment an in vivo MRI scan given

theatlasbuilt inAtlasconstructionWe1047297rst describethe underlyinggen-

erative model which builds on that of Algorithm for atlas construction

and then detail an algorithm to estimate the segmentation using Bayesianinference As in the previous section we will assume that we are

segmenting a left hippocampus If we wish to segment the right hippo-

campus we simply 1047298ip the atlas in the leftndashright direction

Generative model

The built atlascan be used to segment a previously unseen MRI scan

acquired with any type of MRI contrast (monomodal or multimodal)

using the generative model displayed in Fig 6 The 1047297rst layers of the

model are the same as in Fig 4 the atlas which de1047297nes prior probabil-

ities of label occurrences in space is 1047297rst deformed according to the

model proposed in (Ashburneret al 2000) andthen labelsare sampled

at each voxel location to obtain a segmentation L The difference is that

now this segmentation is connected to image intensities through a like-

lihood term for which we assume that a Gaussiandistribution is associ-ated with each label

Inorderto re1047298ect the fact that there is very little contrast between dif-

ferentwhite matter structuresin structuralMR imagesof thebrainwe as-

sume that the 1047297mbria and the cerebral white matter belong to a global

white matter class described by a single Gaussian distribution Likewise

the cerebral cortex amygdala and hippocampal gray matter structures

(para- pre- and subiculum CA1ndash4 GCndashDG HATA) also are assumed to

be part of a global gray matter class The cerebrospinal 1047298uid (CSF) struc-

tures (ventricles hippocampal 1047297ssure) share a class as well The dien-

cephalon thalamus pallidum putamen and choroid plexus each have

independent intensity classes The alveus and molecular layer could in

principle be part of the global white matter class however due to their

thin shape they are often affected by partial voluming so we allow

them to have their own Gaussian parameters as well

Table 3

Mean hippocampal volumes derived from the proposed ex vivo atlas (FreeSurfer v60) the in vivo atlas (FreeSurfer v53) the UPenn atlas (Yushkevich et al 2009) and two histological

studies of thehippocampus(Simic et al 1997 Hardinget al 1998) Allthe volumes arein cubic millimetersThe UPenn atlas is availableat httpwwwnitrcorgprojectspennhippoatlas

we computed its volumes from the most likely labels

Method Age PARA PRE SUB CA1 CA23 CA4 DG Tail ML HATA FIM ALV

Ex vivo atlas 786 51 254 337 520 179 211 244 465 466 50 92 320

In vivo atlas 22ndash89 420 521 330 906 496 350 83

UPenn NA 1574 86 201 167 127

Simica

802 404 591 139 197 59Harding 69 321 529 731 138 169 50

This study considered CA4 and DG a single structurea For this study we left out the AD cases and averaged the volumes from the elderly controls only

Fig 6 Illustration of the generative model of MRI images (monomodal data)




The observed MRI intensity image Y is assumed to have been gener-

ated by sampling a Gaussian distribution at each voxel i parameterized

by the mean and covariance corresponding to its global class

p Y j L eth THORN frac14 prodI

ifrac141

pi y ij μ G lieth THORNΣG lieth THORN

frac14 prod

I

ifrac141

N y i μ G lieth THORNΣG lieth THORN

where G(li) represents the global class corresponding to label li μ G and

ΣG

are the mean and covariance of the global tissue class G N μ Σeth THORN

represents the (possibly multivariate) Gaussian distribution with

mean μ and covariance Σ and y i denotes the intensity in voxel i

The generative model is completed by a prior distribution on the

Gaussian parameters μ G ΣG We use a normal-inverse-Wishart

distribution for each class ndash which is the conjugate prior for a multivar-

iate Gaussian distribution with unknown mean and covariance ndash with

covariance-related hyperparameters set to zero (ie uninformative

prior on the covariance structure)

p μ G

ΣGf g

frac14 prodG p μ GΣGeth THORN

frac14 prodGNIW μ GΣG ΜGν G 0 0eth THORNpropprodG N μ GΜGν Gminus1ΣG

Here ΜG and ν G are the remaining hyperparameters of the

normal-inverse-Wishart distribution Their interpretation is that priorto observing any image data we have an initial guess ΜG of the mean

of tissue class G which is assumed to have been obtained as the sample

mean of ν G observations (note that for ν G = 0 a uniform prior is

obtained)

Segmentation as Bayesian inference

Using the described generative model segmentation is cast as an

optimization problem in a Bayesian framework mdash we search for the

most likely labeling given the probabilistic atlas and the observed

image intensities Exact inference would require marginalizing over

the model parameters x (the mesh deformation) and μ G ΣG which

leads to an intractable integral Therefore we make the approximation

that the posterior distribution of such parameters in light of the atlas

and observed image intensities is heavily peaked This allows us to

1047297rst1047297nd the maximum-a-posteriori(MAP)estimatesof the parameters

and then use these values to derive the segmentation

^ L frac14 argmaxL

p L jY α xr β Keth THORN

asymp argmaxL

p L j^ x ^ μ G

ΣG

n o Y α xr

β K

where the most likely model parameters are given by

^ x ^ μ G

ΣG

n on o frac14 argmax

x μ Gf g ΣGf g

p x μ G

ΣGf gjY α xr

β K

eth7THORN

Using Bayesrulewe rewritethe problem in Eq (7) and obtain the

following objective function for parameter estimation

^ x ^ μ G

ΣG


x μ Gf g Σ Gf g

p Y jα x K μ G

ΣGf g

p xj β xr

Keth THORN p μ G

ΣGf g

frac14

argmax x μ Gf g Σ Gf g

log p x j β xr Keth THORNthorn

XI

ifrac141 log

XG pi y ij μ GΣGeth THORN pi Gjα x Keth THORN

h ithorn

XG

log p μ GΣGeth THORN

eth8THORN

where we have introduced the prior for global tissue class G as

pi Gjα x Keth THORN frac14 sumkisinG pi kjα x Keth THORN WesolveEq (8) by alternately opti-

mizing for the mesh deformation x and the Gaussian parameters

μ G ΣG We update the mesh deformation x by optimizing Eq (8)

directly with a conjugate gradient algorithm and the Gaussian

parameters with an EM algorithm In the E step we perform a probabi-

listic label classi1047297cation for each voxel

ΩGi frac14

pi y ij μ GΣGeth THORN pi Gjα x Keth THORNXG0 pi y ij μ G0 ΣG0eth THORN pi G0jα x K

and in the M step the Gaussian parameters are updated as follows

μ Glarrν GΜG thorn

XI

ifrac141ΩGi y i

ν G thornXI

ifrac141ΩG

i

ΣGlarr

XI

ifrac141ΩG

i y iminus μ Geth THORN y iminus μ Geth THORNt thorn ν G μ GminusΜGeth THORN μ GminusΜGeth THORNt

XI

ifrac141ΩG

i

Once the optimal parameters x ^ μ G

ΣG

n o have been estimated

the (approximately) optimal segmentation argmaxL

p L j^ x ^ μ G

ΣG

n o

Y α xr β KTHORN can be computed voxel by voxel as

li asymp argmaxk

pi y ij μ G keth THORNΣG keth THORN pi kjα x Keth THORN

If we are interested in the volumes of the different structures theirexpected values are given by

V k frac14XI

ifrac141

pi y ij μ G keth THORNΣG keth THORN

pi kjα x Keth THORN

Xk

0 pi y ij μ G k0eth THORNΣG k0eth THORN

pi k0jα x K

eth9THORN

Image preprocessing algorithm initialization and computation of

hyperparameters

To initialize the segmentation algorithm and compute the hyper-

parameters ΜG ν G we use the output from the standard FreeSurfer

pipeline (ldquorecon-allrdquo) which operates on whole brain T1 data at 1 mm

resolution FreeSurfer produces a skull-stripped bias 1047297eld corrected

volume that we use as T1 component of the input to the hippocampalsegmentation algorithm It also produces a segmentation of this whole

brain volume into 36 structures If additional channels ( eg high-

resolution T2) are available they are 1047297rst rigidly coregistered with the

T1 scan with mutual information (FreeSurfers ldquomri_robust_registerrdquo)

using the brain mask provided by FreeSurfer to eliminate the in1047298uence

of non-brain tissue on the alignment The resulting transform is used to

map the (skull-stripped bias 1047297eld corrected) T1 data and its automated

segmentation to the space of the additional scan The mapped segmen-

tation is used to skull strip the additional channels The preprocessed

data from all the available channels is then resampled to the voxel

size at which we desire to compute the segmentation which is equal

to the resolution at which the atlas will be rasterized5

We position the cuboid region that the atlas models by mapping it

to the image to be segmented with an af 1047297ne sum of squares based

registration algorithm (implemented in ldquomri_robust_registerrdquo) The

algorithm uses the binary hippocampal segmentation from FreeSurfer

as target imageand a soft probability mapfor the whole hippocampusndash

computed from the mesh in referencepositionndash as sourceimage for the

registration Henceforth we refer to the region covered by the mapped

atlas cuboid as ldquoatlas region of interest (ROI)rdquo The voxels outside the

atlas ROI are not considered by the segmentation algorithm

In addition to preprocessing the input data and computing the atlas

ROI the segmentation of the brain into 36 structures generated by

FreeSurfer is also used compute the hyperparameters ΜG ν G as

follows for each global class G we 1047297rst 1047297nd all the voxels segmented

5 Converted from the mesh representation to discrete voxels with barycentric

interpolation




as such structure by FreeSurfer Next we set M G to the modality-wise

median intensity of that structure Then we set ν G to the number of

voxels used in the estimation of the median Using the FreeSurfer seg-

mentation from the whole brain improves the estimate of the Gaussian

parameters especially when the number of voxels for a given class is

small within theatlas ROI For instance it is not always easy to estimate

theGaussian parameters of the CSFfrom the atlas ROI partly due to the

presence of the choroid plexus However if we look at the whole brain

such parameters can be easily estimated from the full ventriclesThere are however four classes for which the hyperparameters are

computed in a different manner gray matter white matter alveus

and molecular layer For the gray and white matter since there are so

many voxels labeled as such in the whole brain we only use those

from the hippocampus and neighboring regions in the FreeSurfer

parcellation of each hemisphere This way we take advantage of a rela-

tively large number of voxels to inform the model while eliminating the

drift in the hypermeans M G that could be caused by voxels far away

from the hippocampus due to the MRI bias 1047297eld For the white matter

we use the superior occipital gyrus the orbital part of inferior frontal

gyrus and the opercular part of the inferior frontal gyrus of the corre-

sponding hemisphere For the gray matter we use the parahippocampal

entorhinal and fusiform cortices as well as the whole hippocampus and

amygdala from the corresponding hemisphere

The hyperparameters of the alveus and molecular layer are comput-

ed in a different way because due to their thin shapes they are more

severely affected by the partial volume effect such that the global

white tissue class does not model their intensity distribution correctly

(despite the fact that they are white matter structures) We compute

the hyperparameters of these structures by mimicking the partial vol-

ume effect as follows First we rasterize the mesh at the initial position x at the native resolution (025 mm isotropic) Next we sample a label liat each voxel i from li pi kjα xm

Keth THORN to generate a sample segmenta-

tion L Then we assign to each voxel the mean intensity of its corre-

sponding label while assuming that the alveus and molecular layerbelong to the global white matter class Then we blur this image with

a Gaussian kernel that matches the resolution of this synthetic image

to that of the test scan to segment by setting its FHWM (in voxels) in

each direction to the voxel size of the test scan in that direction divided

by the native voxel size of the atlas (025 mm) Finally M alv and M ML

are set to the median intensity of the 1047297mbria and molecular layer

in the synthetic image whereas we set ν alv and ν ML to the volume of

these two structures provided by the atlas (see Section Statistical atlas

volumes of subregions and sample slices)

Qualitative segmentation results on high resolution T1T2 data from

Winterburn et al (2013)

In this section we show qualitative results on a publicly available

dataset of high resolution T1T2 data The dataset (Winterburn et al

Fig 7 Sampleimages(T1 andT2 weighted) andmanual segmentations of ldquosubject1rdquo from(Winterburn et al2013)(S1ndashS4)Sagittal slices from medialto lateral (C1ndashC9)Coronal slices

from anterior to posterior (R1) 3D rendering of manual segmentation anterior view (R2) 3D rendering inferior view




2013) is a public repository of T1 and T2-weighted scans of 1047297ve subjects

(two males three females ages 29ndash57) acquired on a 3 T GE scanner

with an 8-channel head coil Both theT1 and the T2 scans were acquired

at 06 mm isotropic resolution and then super-sampled to 03 mm iso-

tropic Manual delineations of 1047297ve subregions are also available as part

of the repository CA1 CA23 dentate gyrus molecular layer and

subiculum Note however that a direct evaluation through comparison

of manual and automated segmentations (eg with Dice scores) is not

possible due to the differences between our subregion labeling protocol(described in Manual segmentation of ex vivo MRI data anatomical

de1047297nitions) and theirs Instead we present qualitative results since

high resolution images are available for both the T1 and T2 channels

(see sample slices in Fig 7) we can compare the outputs produced by

the segmentation algorithm on the T1 data the T2 data and both com-

bined When using a single channel in the segmentation y i is a scalar

with the T1 (or T2) intensity and μ G ΣG are also scalars with the

means and variances of the tissue types When we segment both chan-

nels simultaneously y i i s a 2 times 1 vector with theT1 and T2 intensities at

spatial location i while the means μ Gare2 times 1 vectors and the covari-

ances ΣG are 2 times 2 matrices In this experiment the work resolution is

set to 03 mm mdash equal to the voxel size of the input scans

Figs 8 and 9 show sample segmentations from ldquosubject 3rdquo in

the dataset using the T1 scan alone the T2 scan alone and both scans

simultaneously segmentationsfrom theother foursubjectsin thedataset

are provided in the supplementary material (Fig 20 and Fig 21) Note

that we haveremoved from the1047297nal segmentationthe neighboringstruc-

tures of the hippocampus as well as the alveus showing very little con-

trast in in vivo MRI due to its thin shape its automated segmentation is

often unreliable The method effectively adapts to the MRI contrast in

each case successfully segmenting the hippocampus in all three

scenarios The segmentation based solely on the T1 image accurately cap-

tures the global shape of the hippocampus but often under-segments the

molecular layer (marked with blue arrows in the 1047297gures) as well as cysts

and CSF pockets (red arrows) which are hardly visible in T1 These fea-

tures are correctly segmented in the T2 image which on the other

hand captures the global shape of the hippocampus less accurately than

the T1 scan due to its poorer contrast between gray and white matter

(see regions marked with yellow arrows in the 1047297gures) The output

based on multimodal MRI data takes advantage of the information fromboth channels to produce a smoother more accurate segmentation that

combines the advantages of the T1 and T2 MRI contrasts

Figs 8 and 9 also show the corresponding manual segmentations

from the original article (Winterburn et al 2013) The agreement

between the manual and automated segmentations is fair in general

but some differences can be found in the areas where the segmentation

is poorly supported by the image contrast (eg the medial digitation

in Fig 8) and also in the hippocampal regions where our de1047297nitions of

the subregionsand theirsdisagree Firstsome of the labelsof our proto-

col do not exist in their labeling scheme tail 1047297mbria GCndashDG HATA

parasubiculum and presubiculum Second even though the agreement

of the protocols is good in the superior part of the hippocampus (see

3D renderings in Fig 10) large differences in thede1047297nition of the subre-

gions can be generally observed in the inferior part our subiculum is

largely part of their CA1 while our presubiculum and parasubiculum

correspond approximately to their subiculum

Quantitative results on ADNI T1T2 data

In this section we present segmentation results on a dataset of

30 T2 MRI scans from the Alzheimers Disease Neuroimaging Initiative

Fig 8 Sample coronal slices of ldquosubject 3rdquo from (Winterburn et al 2013) from anterior (left) to posterior (right) Top row T1 image Second row T2 image Third row segmentation

computed with theT1 scan Fourth row segmentation computed with T2scan Fifth row segmentation computedwithT1 andT2 scans simultaneously overlaid on theT2 imagesBottom

row manual segmentation from the original study The red arrow marks a CSF pocket the blue arrows mark the molecular layer and the yellow arrow marks the medial digitation




(ADNI) database (adniloniuscedu) The ADNI was launched in 2003 by

the National Institute on Aging the National Institute of Biomedical Im-

aging and Bioengineering the Food and Drug Administration private

pharmaceuticalcompanies and non-pro1047297t organizations as a $60million

5-year public-private partnership Themain goalof ADNIis to testwheth-

er MRI positron emission tomography (PET) other biological markers

and clinical and neuropsychological assessment can be combined to ana-

lyze theprogressionof MCI and early AD Markers of earlyAD progression

can aid researchers and clinicians to develop new treatments and moni-

tor their effectiveness as well as decrease the time and cost of clinical

trials The Principal Investigator of this initiative is Michael W Weiner

MD VA Medical Center and University of California mdash San Francisco

ADNI is a joint effort by co-investigators from industry and academia

Subjects have been recruited from over 50 sites across the US andCanada The initial goal of ADNI was to recruit 800 subjects but ADNI

has been followed by ADNI-GO and ADNI-2 These three protocols have

recruited over 1500 adults (ages 55ndash90) to participate in the study

consisting of cognitively normal older individuals people with early or

late MCI and people with early AD The follow up duration of each

group is speci1047297ed in the corresponding protocols for ADNI-1 ADNI-2

and ADNI-GO Subjects originally recruited for ADNI-1 and ADNI-GO

had the option to be followed in ADNI-2 For up-to-date information

see httpwwwadni-infoorg

The choice of the subset of ADNI scans for this analysis was motivat-

ed by the fact that these are the exact same images that were used in

(Mueller et al 2013) which includes MCI classi1047297cation results derived

from segmentations produced by a number of automated and semi-

automated methods as well as a manual delineation protocol that

Fig 9 Sample sagittal slices of ldquosubject 3rdquo from Winterburn et al (2013) from medial (left) to lateral (right) See caption of Fig 8 for an explanation of the different rows The red arrow

marks a CSF pocket the blue arrows mark the molecular layer and the yellow arrows mark segmentation errors in the whole hippocampal shape

Fig 103D renderings of segmentations of thehigh-resolution T1T2 data (a)Manual seg-

mentation from Winterburn et al (2013) anterior view (b) Automated segmentation

using T1 and T2 volume simultaneously anterior view (cndashd) Inferior view of (andashb)




only considers 1047297ve coronal slices in the body of the hippocampus

(Mueller et al 2010) Using this dataset enables direct comparison of

our results with those from (Mueller et al 2013) The 30 scans corre-

spond to an acquisition protocol that has recently been added to theADNI study with the following parameters TR = 8020 ms TE =

50 ms resolution 04times 04times 20 mm (coronal) 24ndash30 slices acquisition

time 8 min Of the 30 scans 16 correspond to subjects with early MCI

(ages 743 plusmn 76) and the other 14 to age-matched healthy controls

(ages 708 plusmn 72) Since these scans are part of the ADNI the corre-

sponding T1-weighted images (sagittal 3D MPRAGE scans at 1 mm res-

olution) are also available A samplecoronal slice of a T2 scan from ADNI

is shown in Fig 11a and a sagittal slice (overlaid on the corresponding

T1-weighted scan) in Fig 11b The sagittal slice shows how narrow the1047297eld of view of these scans sometimes is failing to cover the whole

hippocampusTo segment these ADNI data we take advantage of not only the high-

resolution T2 images but also the 1 mm isotropic T1 scans which provide

complementary information On the one hand the T2 data have good

contrast between subregions but large slice separation and a narrow

1047297eld of view On the other hand the T1 scans provide isotropic data

throughout the whole brainmdash though with little information on the sub-

regions Therefore we segment both channels simultaneously ie y i

Fig 11(a)Coronal slice from T2scan from ADNI andclose-upof thehippocampi(b) Sagittal slice from a T2scan fromADNIoverlaidon thecorrespondingT1 volumeThisview illustrates

the limited 1047297eld of view of the T2 scans in ADNI The in-plane resolution of the T2 scans is 04 mm and the slice separation is 2 mm The T1 scans are 1 mm isotropic

Fig 12 Inputs (T1 T2) and segmentationsfor 1047297ve representative casesof the ADNI T1T2 dataset The resolution of the T1 scans is 1 mm isotropic whereas the T2 scans have04 mm in-

plane resolution (coronal) and 2 mm slice separation (a) A cyst being segmented as hippocampal 1047297ssure (b) A case with good contrast well-segmented (c) A case where the partial

volume effect has misguided the segmentation suchthat part of the lateralventricle (marked by the arrow) is labeled as CA23 (d)A casewith poor contrast the internal segmentation

ofthe hippocampus islargelydetermined bythe prior (e) A case inwhich the1047297eldof view ofthe T2scandoesnot coverthewholehippocampus the segmentation ofthe tail relies solely

on the T1 data All slices are coronal except for (e) which is sagittal More slices are displayed in the supplementary material (Fig 22)




and μ Garea2 times 1 vectors andthe covariances ΣGarea2 times 2 matrices

The information of the T1 scan is particularly important when the T2 in-

tensities are missing for some hippocampal voxels due to the limited

1047297eld of view of the T2 scan (as in Fig 11b where the hippocampal tail is

only visible in the T1 scan) In that case the equations for Gaussian pa-rameter optimization in Algorithm for segmenting an in vivo scan needs

to be modi1047297ed in order to account for this missing information mdash see de-

tails in Appendix A In this experiment theworkresolution is 04 mm iso-

tropic mdash equal to the in-plane resolution of the T2 images

Fig 12 shows slicesfrom automated segmentations of some represen-

tative cases in the ADNI T1T2 dataset When the quality of the scan is

good and the molecular layer is visible (as in Fig 12b) the model gener-

ally produces a good segmentation However mistakes occur sometimes

due to image artifacts In Fig 12c CSF and white matter mix in the same

voxel making it resemble gray matter (partial volume effect) and thus

misleading the segmentation algorithm In Fig 12d motion artifacts ren-

der the molecular layer invisible In such cases the internal boundaries of

the hippocampus are mostly determined by the statistical atlas (rather

than image intensities) and to a lesser extent by other features such ascysts or the hippocampal 1047297ssure Finally Fig 12e shows an example of

when the lower-resolution T1 is most useful which is when the 1047297eld of

view of the T2 scan does not cover the whole hippocampus In that

case the algorithm can still produce a seamless smooth segmentation

of the whole hippocampal formation

Direct evaluationof the produced segmentations wouldrequire manu-

al delineations for the T2 data made with the ex vivo protocol from Section

Manual segmentation of ex vivo MRI data anatomical de1047297nitions which

arenotavailable(and would be extremely dif 1047297cult to make due to the lack

of resolution) Therefore we use indirect evaluation methods instead

based on assessing the ability of the automatically estimated subregion

volumes to discriminate two populations (MCI and elderly controls) in a

group analysis framework First we compute the subregion volumes

from thesoft segmentations with Eq (9) Then we correct these estimates

for age and intracranial volume (ICV) by regressing them out with a gen-

eral linear model This step is important because the subregion volumes

are strongly correlated with these two variables which can easily con-

found the analysismdash subjects with large ICV andor of younger age are ex-

pected to have larger hippocampi see for instance (Mueller et al 2010)Moreover such correction was used in (Mueller et al 2013) so we used

this correction as well in order to directly compare the results

Once the corrected volumes have been computed we compare the

volumes of the two groups for each subregion independently with

unpaired two-sample t-tests Since we have a strong hypothesis that

the volume of the subregions does not increase in MCI or AD (except

for the 1047297ssure which tends to increase in AD) we can conduct one-

tailed tests mdash for the 1047297ssure we just invert the sign of the test In addi-

tion we also conduct a power analysis in which we compute the sample

size required by the test to have a power6 of 050ndash which was the value

used in (Mueller et al 2013) ndash as well as the power provided by theac-

tual sample size of the dataset

The group analysis of the subregion volumes is summarized in

Table 4 The table also includes two sets of results reported in (Muelleret al 2013) a group analysis for subregion volumes derived from the

manual segmentation protocol and another group analysis for the

volumes given by the semiautomated algorithm from (Yushkevich

et al 2010) Our algorithm1047297nds differences in the left and right CA1 mo-

lecular layer dentate gyrus CA4 and whole hippocampus as well as the

left 1047297mbria and CA23 region The manual annotations (for which the vol-

umes were left-right averaged) show differences in CA1 and dentate

gyrus whereas Yushkevichs semi-automated method yields signi1047297cant

differences in CA1ndash3 and CA4-DG mdash also with leftndashright averaged vol-

umes Our results are quite consistent with theirs given that their

methods do notconsider thesmaller subregions containedin ourprotocol

In addition our results show strong consistency with prior work using

6

De1047297ned as the probability of correctly rejecting the null hypothesis when it is false

Table 4

Group analysis for the hippocampal subregion volumes of MCI subjects (n = 14) and elderly controls (n = 16) in the ADNI T1T2 data The samples sizes correspond to signi1047297cance

criterion = α = 005 power = 1-β = 050 mdash which were the values used in (Mueller et al 2013) The p-values correspond to unpaired one-tailed two-sample t-tests and are

not corrected for multiple comparisons Signi1047297cant values (α b 005) are marked in bold For Mueller et al and Yushkevich et al some of the de1047297nitions of the subregions are different

from ours (Manual segmentation of ex vivo MRI data anatomical de1047297nitions) In these cases their de1047297nitions are shown in parentheses Note that the ex vivo atlas does not include

the entorhinal and perirhinal cortices these are already analyzed by FreeSurfer (Fischl et al 2009 Augustinack et al 2013 2002)

Structures Left (this study) Right (this study) LR average

(Mueller et al manual)

LR average

(Yushkevich et al)

p value Sample size Power p value Sample size Power Sample size Power Sample size Power

Parasubiculum 015 73 027 022 134 019

Presubiculum 021 121 020 008 41 040

Subiculum 014 66 029 018 95 023 25 057 59 027

CA1 003 24 058 002 18 069 11 095 10 (CA123) 099

CA23 002 18 071 010 47 036 27 (CA12) 055

CA4 003 23 059 004 25 057 26 (CA4DG) 042

GCndashML ndashDG 002 20 065 001 16 075 14 (CA3DG) 088

Molec layer 002 20 067 005 28 052

Fimbria 002 19 068 004 26 055

Hippo 1047297ssure 045 N1000 010 026 187 017

HATA 020 111 021 007 36 043

Hippo tail 045 N1000 010 049 N1000 010

Whole hippo 004 27 054 004 25 056

Entorhinal 500 007 96 018

Perirhinal 223 010

Table 5

Comparing subregion volume measurements from different modalities (only T1 vs combined T1T2) through their ability to discriminate MCI subjects fromelderly controls in the ADNI

T1T2 data (measured with p-values of unpaired one-tailed two-sample t-tests) Signi1047297cant values (without correction for multiple comparisons) are marked in bold

Side Modality Parasu Presub Sub CA1 CA23 CA4 GCndashDG Mol lay Fimb Hipp 1047297ss HATA Tail Whole hippo

Left T1 010 047 023 008 012 008 011 009 004 030 030 044 008

T1 + T2 015 021 014 003 002 003 002 002 002 045 020 045 004

Right T1 034 047 032 010 025 008 006 012 007 035 021 028 010

T1 + T2 022 008 018 002 010 004 001 005 004 026 007 049 004




manual and semi-automated segmentation procedures on the same type

of images even if direct comparison across studies is not possible due to

differences in labeling protocols the differences in CA1 CA4ndashDG and

whole hippocampus have been previously described in (Pluta et al

2012)which is based on the method from (Yushkevich et al 2010)Inad-

dition our algorithm also 1047297nds statistically signi1047297cant differences in the

molecular layer and 1047297mbria a decline of the former which shows great

discrimination power in both the left and right hippocampus has been

previously described in the literature (Kerchner et al 2010 2012)In order to quantify the impact of the high-resolution T2 scan in the

segmentation we also compare the ability of the subregion volumes to

discriminate the two groups when they are measured with the com-

bined T1T2 data and when they are derived from the T1 images

alone Table 5 displays the p-values of the corresponding t-tests

which show that the measurements using both modalities better cap-

ture the differences in the subregions between the two groups When

only the T1 scans are used the resolution is insuf 1047297cient to distinguish

the molecular layer In this case the volumes of the subregions depend

largely on the volume and shape of the whole hippocampus which

reduces the ability of the individual subregions to separate the two

groups Only the 1047297mbria which is visible at 1 mm resolution seems to

provide comparable discrimination power after the high-resolution T2

scan is removed from the analysis

Quantitative results on standard resolution ADNI T1 data

Here we present results on a dataset of standard resolution scans

from the ADNI The dataset consists of 400 baseline T1 scans from the

study for which high-resolution T2 data are not available These scans

were acquired with MPRAGE sequences at 1 mm isotropic resolution

The MRI data were processed through the standard FreeSurfer pipeline

including the current hippocampal sub1047297eld module which is useful

to compare the segmentations yielded by the in vivo atlas with those

produced by the ex vivo atlas we are introducing in this study This hip-

pocampal sub1047297eld processing did not complete successfully for 17 scans

(due to software crashes) which were removed from the analysis

The demographics of the remaining 383 subjects are as follows 562

elderly controls (age 761 plusmn 56 years) 438 AD patients (age 755 plusmn76) 536 males (ages 761 plusmn 56) 464 females (ages 759 plusmn 68)

The resolution at which we rasterized the atlas and computed the

segmentation in this experiment was 13 mm

As in Section Quantitative results on ADNI T1T2 data we use the

performance in a group analysis as a surrogate for segmentation quality

In this case we validate the segmentation by comparing the subregion

volumes of AD patients and elderly controls As in the previous section

the resolution of the ADNI T1 scans is insuf 1047297cient to distinguish the

molecular layer making the segmentation much lessreliable Therefore

the volumes of the subregions are largely determined by the whole hip-

pocampal volume such that most subregionsshow large discriminative

power but little differentiation between the subregions is observed

This is illustrated by the results in Table 6 which displays effect sizes

for each subregion ndash for both the in vivo and ex vivo atlases ndash measuredwith Cohens d ie the difference between two means divided by

the standard deviation of the data We used effect sizes rather than

p-values in this experiment because due to the large sample size and

strong effect all p-values were very small and the differences between

the effects on the subregions were harder to appreciate Large or very

large effect sizes are observed for all subregions except for the hippo-

campal 1047297ssure The effect sizes given by the segmentations based on

the in vivo and ex vivo atlases are quite similar even though they are ndash

on average ndash slightly larger for the ex vivo atlas The main difference

between the results of the two atlases is the effect for CA1 which is

smaller in the in vivo version

For the reason mentioned above (ie the lack of internal contrast of

the hippocampus at 1 mm resolution) the results in Table 6 must be

interpreted with caution Therefore we use another method to separate

the two populations based on a statistical classi1047297er that discriminates

the groups using all the subregion volumes simultaneously The process

is the following First we average the subregion volumes from the left

and right hippocampi as this boosts the power of the analysis without

compromising the generalization ability of the classi1047297er by increasingthe dimensionality of the data Subsequently we perform a correction

for age and ICV for each subregion independently in the same way as

described in Section Quantitative results on ADNI T1T2 data Then

we concatenate all the subregion volumes of each subject into a vector

and use it as input to a linear discriminant analysis (LDA) classi1047297er

(Fisher 1936) The use of a simple linear classi1047297er such as LDA ensures

that the classi1047297cation accuracy is mainly determined by the quality of

the input data (ie the subregion volumes) rather than stochastic vari-

ations in the classi1047297er

We compared theperformance of thesegmentationsgiven by thenew

ex vivo atlas with those produced by thein vivo atlas inFreeSurfer v53 (we

used the ldquooff-the-shelf rdquo implementation of the segmentation algorithm)

We used two metrics in the comparison the area under the receiver op-

erating characteristic (AUROC) of the classi1047297ers and their maximum clas-si1047297cation accuracy The latter is given by the threshold corresponding to

Table 6

Effect sizes (Cohens d) of the group analysis for the hippocampal subregion volumes in

the AD discrimination task Larger effect sizes correspond to larger differences between

the two groups

Structures Left Right

Ex vivo In vivo Ex vivo In vivo

Parasubiculum 137 106

Presubiculum 199 194 180 148

Subiculum 189 178 189 154

CA1 199 090 182 067

CA23 158 139 159 124

CA4 179 153 180

GCndashML ndashDG 181 184

Molecular layer 209 203

Fimbria 060 070 039 067

Hippocampal 1047297ssure 013 015 021 017

HATA 145 151

Hippocampal tail 171 145 164 124

Whole hippocampus 211 182 208 149

Fig 13 ROC curves for theAD discrimination taskusing a LDAclassi1047297er on the hippocam-

palsubregionvolumes estimated by the ex vivo atlas (FreeSurferv60)and the in vivo atlas

(FreeSurfer v53 and earlier) as well as for discrimination based on whole hippocampal

volume as estimated by FreeSurfer (ldquoasegrdquo) and by the ex vivo atlas (adding up the

volumes of the subregions)




the ldquoelbowrdquo of the receiver operating characteristic (ROC) curve ie the

point closest to FPR = 0 TPR = 1 We used leave-one-out cross-

validation to compute the ROC Signi1047297cance in the difference in AUROCs

wasassessed with a non-parametric test (DeLonget al 1988) In addition

we also compared a classi1047297er based solelyon whole hippocampal volume

which allows us to quantify the bene1047297t of using the subregion volumes

with respect to the whole hippocampus We used two different estimates

of the volume the sum of the subregion volumes given by the ex vivo atlas

(except for the1047297ssure)and the whole hippocampus estimate provided by

FreeSurfers automated segmentation (ldquoasegrdquo)

The ROC curves for the AD vs elderly controls discrimination task are

shown in Fig 13 whereas the areas under the curves and accuracies aredisplayed in Table 7 The ex vivo atlas outperforms the in vivo counterpart

especially around the elbow of theROC which is theregion where a clas-

si1047297er typically operates The increment in the AUROC is moderate (14)

but statistically signi1047297cant ( p b 002) This indicates that the segmenta-

tions based on the ex vivo atlas provides more informative estimates of

the volumes than those based on the in vivo version Both the in vivo

and the ex vivo atlas outperform the whole hippocampal segmentations

which yields 82 (ldquoasegrdquo) and 84 (sum of subregions) classi1047297cation ac-

curacy The difference in AUROC between the ex vivo atlas and the whole

hippocampal segmentations is noteworthy (59 and 40 respectively)

and statistically signi1047297cant ( p b 001 in both cases) These results indicate

that the subregion volumes carry useful information even when the im-

ages display limited contrast on the internal subregion boundaries Auto-

mated segmentations of a test scan are shown in Fig 14

Discussion and conclusion

In this paper we have presented the construction of a statistical atlas

of the hippocampus at the substructure level using a combination of

ex vivo and in vivo MRI data Manual annotations of the hippocampal

subregions (on ex vivo images) and of the neighboring structures (on

in vivo data) were combined into a single atlas using a novel algorithm

Using Bayesian inference the constructed atlas can be used to

automatically segment the hippocampal subregions in in vivo MRI

scans Given the generative nature of the framework the segmentation

method is adaptive to MRI contrast and can naturally handle multi-

contrast inputs The segmentation algorithm was validated on three

publicly available datasets with varying MRI contrast and resolution

(Winterburn ADNI T1T2 and ADNI T1) We plan to release the atlas

as part of the next release of FreeSurfer replacing the in vivo atlas of

the hippocampal sub1047297eld module in the current version of the package

(v53)The presented atlas improves previous high-resolution atlases of the

hippocampus in several directions Compared with the in vivo version

the ex vivo atlas was built upon data of much higher resolution which

allowed us to accurately trace the molecular layer with very little

dependence on geometric criteria As a consequence the atlas yields sub-

region volumes that better matched values to previously reported histo-

logical studies (Simic et al 1997 Harding et al 1998) Compared to the

ex vivo UPenn atlas presented in (Yushkevich et al 2009) we have ex-

tended their work in four directions First we have scanned the samples

at 13 mm isotropic resolution on average which yields voxels four

times smaller than those in their atlas Second we have modeled a larger

number of hippocampal structures (13 vs 5) Third we have used a great-

er number of cases (15 vs 5) And fourth our ex vivo atlas modelsnot only

the hippocampal formation but also the surrounding structures This is a

critical difference since it enables us to use the atlas in a Bayesian frame-

work to directly segment in vivo MRI data of arbitrary contrast properties

Wehave testedthe ability of thevolumes derived from automatedseg-

mentations given by the atlas to 1047297nd differences between controls and

subjects with MCI and AD Using high-resolution T2 data we can reliably1047297t the atlas to the internal structure to the hippocampus this was not pos-

sible with the previous atlas in FreeSurfer (v53 or earlier) which did not

model the molecular layer In a group experiment with MCI subjects and

controls our new method reproduced the results of previous manual

and semi-automated algorithms Moreover we found differences in the

molecular layer and the 1047297mbria which the aforementioned methods do

not segment Since the molecular layer is a thin structure it is possible

that the lower volume estimates are due to motion artifacts to which

the MCI group is more susceptible Regarding the 1047297mbria visual inspec-

tion of the images reveals that the appearance of this subregion tends toshift towards that of gray matter in aging and AD It is important to note

that we cannot conclude from our volumetric analysis whether this is a

true biological process or the result of motion artifacts

We also used the atlas to segment standard resolution (1 mm) T1

data In this case the molecular layer is not visible and the 1047297tting of the

internal structure of the atlas mostly relies on the prior information

encoded in it Therefore volumetric results from individual subregions

must be interpreted with caution Still we hypothesize that the segmen-

tations will be very useful as seed and target regions in functional and

Fig 14 Automated segmentation of the hippocampal subregions of a sample case from the ADNI T1 dataset (T1-weighted 1 mm isotropic) using FreeSurfer automated segmentation

(ldquoasegrdquo) as well as the in vivo and ex vivo atlases a) Slices of the segmentation b) 3D renderings of their shape The color map is the same as in Figs 2 and 5

Table 7

Accuracy and area under the curve for the AD discrimination task

Atlas Accuracy

at elbow

AUROC

Whole hippocampus (ldquoasegrdquo FreeSurfer v53) 821 0887

Whole hippocampus

(adding up the volumes of the subregions)

840 0901

In vivo (FreeSurfer v53) 863 0917

Ex vivo (this study and FreeSurfer v60) 880 0931




diffusionMRIstudies in which the large voxel sizes make the analysis less

sensitive to small segmentation errors Moreover we have shown that

the subregion segmentation carries despite the lack of internal contrast

of the hippocampus useful information that is not conveyed by its

whole segmentation the ex vivo atlas signi1047297cantly outperforms the

in vivo atlas in the AD classi1047297cation task which in turns signi1047297cantly

outperforms the segmentation of the whole hippocampus

The segmentation algorithm runs in approximately 20 min on a

desktop computer mdash

approximately twice as long when the input con-sists of two MRI modalities This is in contrast with multi-atlas methods

which are currently used in hippocampal subregion segmentation ndash

suchas (Yushkevich et al 2010) ndashwhich are intrinsically slow (typically

10ndash20 h) due to the need to nonlinearly register a number of atlases to

the test scan On the other hand our algorithm requires at this point

that the data have been processed with thestandardFreeSurfer pipeline

which takes approximately 10 h on a single core

A limitation of the atlas presented in this study is that even with

ultra-high resolution MRI there are boundaries that cannot be seen

in the training data eg the interfaces between the CA 1047297elds along the

pyramidal layer of the hippocampus or the CA4GCndashDG interface This

remains an open problem in the hippocampal subregion MRI literature

in which the discrepancy and variability in subregion de1047297nitions

remains rather large (Yushkevich et al in press) This effect can be im-

mediately noticed by comparing the heterogeneous manual annota-

tions used in works such as (Yushkevich et al 2009 2010

Winterburn et al 2013 Mueller et al 2007 2010 Van Leemput et al

2009 Wisse et al 2012) Another potential limitation of the proposed

atlas is that it was built from manual delineations in elderly subjects

only Therefore the atlas might include slight hippocampal atrophy

that could decrease its applicability to studies of younger populations

Future work will follow four directions First we will evaluate the

usefulness of the segmentations on 1 mm data as seed and target

regions on diffusion and functional MRI studies Second we plan to

extend the atlas to include the hippocampal tail ndash which will require

a careful histologic analysis of the autopsy samples ndash and also other

subcortical structures of interest such as the thalamic and amygdaloid

nuclei Due to the generative nature of the segmentation framework

we are not constrained to derive the manual delineations from MRIdata histology or optical coherence tomography can be used too

(Augustinack et al 2014 Magnain et al 2014) Third we will use

Bayesian techniques to automatically infer the most likely value of the

mesh1047298exibility parameterβ which controls the tradeoff between accu-

racy and robustness And fourth we would like to include explicit

models of the partial volume effect which makes it very challenging

to accurately describe thin white matter structures such as 1047297mbria

and the molecular layer In this study we tackled this problem by guid-

ing the image intensity distributions of these structures with

hyperparameters derived from subject-speci1047297c simulations of partial

voluming However we believe that explicitly incorporating the partial

volumeeffect in the model for instanceas in (VanLeemput et al2003)

will further increase the accuracy of our segmentations

Acknowledgments

Support for this research was provided in part by the National

Center for Research Resources (P41EB015896 and the NCRR BIRN

Morphometric Project BIRN002 U24 RR021382) the National Insti-

tute for Biomedical Imaging and Bioengineering (R01EB013565

R01EB006758) the National Institute on Aging (AG022381

5R01AG008122-22 K01AG028521 BU Alzheimers Disease Center

P30AG13846 BU Framingham Heart Study R01AG1649) the National

Center for Alternative Medicine (RC1 AT005728-01) the National

Institute for Neurological Disorders and Stroke (R01 NS052585-01

1R21NS072652-01 1R01NS070963 R01NS083534) and was made

possible by the resources provided by Shared Instrumentation Grants

1S10RR023401 1S10RR019307 and 1S10RR023043 Additional

support was provided by The Autism amp Dyslexia Project funded by the

Ellison Medical Foundation by the NIH Blueprint for Neuroscience

Research (5U01-MH093765) which is part of the multi-institutional

Human Connectome Project and the Finnish Funding Agency for

Technology and Innovation (ComBrain) JEI acknowledges 1047297nancial

support from the Gipuzkoako Foru Aldundia (Fellows Gipuzkoa Pro-

gram) This research was also supported by NIH grants P30-AG010129

and K01-AG030514 as well as the ADNI 2 add-on project ldquoHippocampal

Sub1047297

eld Volumetryrdquo

(ADNI 2-12-233036) The authors would also liketo acknowledge Rohit Koppula and Lianne Cagnazzi for their help

with the manual segmentation of the ex vivo MRI data and Susanne

Mueller and Paul Yushkevich for their help with the comparison with

their methods (Table 4)

The collection andsharing of the MRI data used in theevaluation was

funded by the Alzheimers Disease Neuroimaging Initiative (ADNI) (Na-

tionalInstitutesof HealthGrantU01 AG024904) and DODADNI(Depart-

ment of Defense award number W81XWH-12-2-0012) ADNI is funded

by the National Institute on Aging the National Institute of Biomedical

Imaging and Bioengineering and through generous contributions from

the following Alzheimers Association Alzheimers Drug Discovery

Foundation BioClinica Inc Biogen Idec Inc Bristol-Myers Squibb Com-

pany Eisai Inc Elan Pharmaceuticals Inc Eli Lilly and Company F

Hoffmann-La Roche Ltd and its af 1047297liated company Genentech Inc GE

Healthcare Innogenetics NV IXICO Ltd Janssen Alzheimer Immuno-

therapy Research amp Development LLC Johnson amp Johnson Pharmaceuti-

cal Research amp Development LLC Medpace Inc Merckamp Co Inc Meso

Scale Diagnostics LLC NeuroRx Research Novartis Pharmaceuticals

Corporation P1047297zer Inc Piramal Imaging Servier Synarc Inc and

Takeda Pharmaceutical Company The Canadian Institutes of Health Re-

search is providingfundsto support ADNI clinicalsitesin Canada Private

sector contributions are facilitated by the Foundation for theNational In-

stitutes of Health(wwwfnihorg) The grantee organizationis theNorth-

ern California Institute for Research and Education and the study is

coordinated by the Alzheimers Disease Cooperative Study at the Univer-

sity of California San DiegoADNI data aredisseminatedby theLaborato-

ry for Neuro Imaging at the University of Southern California

Appendix A Estimation of Gaussian parameters with missing data

Inthe segmentation of a multimodal test scan it can happen that the

MRI data for some channels are missing at a given voxel (as in Figs 11b

or 12e) In that case the M step of the Gaussian parameter estimation

(Section Algorithm for segmenting an in vivo scan) becomes compli-

cated Instead we use a generalization of the EM algorithm called ldquoEx-

pectation Conditional Maximizationrdquo (ECM) (Meng and Rubin 1993)

in which the M step is replaced by two iterative conditional maximiza-

tion (CM) steps that update the means and covariance matricesrespec-

tively Let y io and y i

m represent the observed and missing parts of vector

y i respectively let μGo(i) and μG

m(i) represent the corresponding parts of

the meanμG letΣGo(i)ΣG

m(i) represent the corresponding parts of the co-

variance matrix ΣG and let ΣGmo(i) be the part of the covariance matrix

describing the cross-correlation between the observed and missingcomponents of y i The update of the mean is then


XI

ifrac141ΩG

i ~ y i

ν G thornXI

ifrac141ΩG

i

where ~ y oi frac14 y oi ~ y

mi frac14 μm ieth THORN

G thorn Σmo ieth THORNG Σ

o ieth THORNG

h iminus1 y oiminusμ

o ieth THORNG

and the update of the covariance is

ΣGlarr

XI

ifrac141ΩG

i ~ y iminus μ Geth THORN ~ y iminus μ Geth THORN

t thorn ~Ψi

h ithorn ν G μ GminusΜGeth THORN μ GminusΜGeth THORNt

XI

ifrac141

ΩG

i




where ỹ i is de1047297ned the same way as above and the matrix ~Ψi has

observed and missing parts ~Ψo

i frac14 0 and ~Ψm

i frac14 Σm ieth THORNG minusΣ

mo ieth THORNG Σ

o ieth THORNG

h iminus1

Σmo ieth THORNG

h it (with the part describing their cross correlation equal to

zero) The E step of the ECM algorithmis thesameas in the EM counter-

part with the difference that the likelihood term is now evaluated as

pi y ij μ GΣG

frac14 N y o

i μo ieth THORN

G l ieth THORNΣo ieth THORNG l ieth THORN

h i

In the speci1047297c casethat the test has two channelsand one of themisalways observedmdash which is the case of the experiments of the ADNI T1

T2 data in Section Quantitative results on ADNI T1T2 data it can be

shown (Provost 1990) that the M step is closed form which leads to

faster convergence of the algorithm In our implementation of the pre-

sented Bayesian segmentation algorithm we use these update equa-

tions whenever it is possible mdash including the experiments with the

ADNI T1T2 data in this paper

Appendix B Supplementary data

Supplementary data to this article can be found online at httpdx

doiorg101016jneuroimage201504042

References

Acsaacutedy L Kaacuteli S 2007 Models structure functionthe transformation of corticalsignalsin the dentate gyrus Prog Brain Res 163 577ndash599

Adler DH Pluta J Kadivar S Craige C Gee JC Avants BB et al 2014 Histology-de-rived volumetric annotation of the human hippocampal sub1047297elds in postmortemMRI NeuroImage 84 505ndash523

Apostolova L Dinov I Dutton R Hayashi K Toga A Cummings J et al 2006 3Dcomparison of hippocampal atrophy in amnestic mild cognitive impairment andAlzheimers disease Brain 129 (11) 2867ndash2873

Arnold S Hyman B Flory J Damasio A Van Hoesen G 1991 The topographical andneuroanatomical distribution of neuro1047297brillary tangles and neuritic plaques in thecerebral cortex of patients with Alzheimers disease Cereb Cortex 1 (1) 103ndash116

Ashburner JT Friston KJ 2001 Computational Neuroanatomy University of LondonAshburner J Andersson J Friston K 2000 Image registration using a symmetric

priormdashin three dimensions Hum Brain Mapp 9 (4) 212ndash225AugustinackJC van der Kouwe AJ Blackwell ML Salat DH Wiggins CJ Frosch

MP et al 2005 Detection of entorhinal layer II using Tesla magnetic resonance im-aging Ann Neurol 57 (4) 489ndash494

AugustinackJCHuberKE StevensAA RoyM FroschMP van derKouweAJ et al2013 Predicting the location of human perirhinal cortex Brodmanns area 35 fromMRI Neuroimage 64 32ndash42

Augustinack JC Helmer K Huber KE Kakunoori S Zoumlllei L Fischl B 2010 Direct vi-sualizationof theperforantpathway in thehuman brain with ex vivodiffusion tensorimaging Front Hum Neurosci 4 42

Augustinack J Magnain C Reuter M van der Kouve A Boas D Fischl B 2014 MRIparcellation of ex vivo medial temporal lobe NeuroImage 93 (2) 252ndash259

Boccardi M Ganzola R Bocchetta M Pievani M Redol1047297 A Bartzokis Get al 2011 Sur-vey of protocols for themanualsegmentationof thehippocampus preparatorysteps to-wards a joint EADC-ADNI harmonized protocol J Alzheimers Dis 26 (Supl 3) 61ndash75

Braak H Braak E 1991 Neuropathological stageing of Alzheimer-related changes ActaNeuropathol 82 (4) 239ndash259

Braak E Braak H 1997 Alzheimers disease transiently developing dendritic changesin pyramidal cells of sector CA1 of the Ammons horn Acta Neuropathol 93 (4)323ndash325

Brady D Mufson E 1991 Alz-50 immunoreactive neuropil differentiates hippocampalcomplex sub1047297elds in Alzheimers disease J Comp Neurol 305 (3) 489ndash507

Burggren A Zenh M Ekstrom A Braskie M Thompson P Small G et al 2008Reduced cortical thickness in hippocampal subregions among cognitively normalapolipoprotein E e4 carriers NeuroImage 41 (4) 1177ndash1183

Caviness V Filipek P Kennedy D 1989 Magnetic resonance technology in human brainscience blueprint for a program based upon morphometry Brain Dev 11 (1) 1ndash13

CendesF AndermannFGloor PEvans AJones-GotmanM WatsonCet al 1993 MRIvolumetric measurement of amygdala and hippocampus in temporal lobe epilepsyNeurology 43 (4) 719ndash725

Chupin M Geacuterardin E Cuingnet R Boutet C Lemieux L Leheacutericy S et al2009 Fully au-tomatic hippocampus segmentation and classi1047297cation in Alzheimers disease and mildcognitive impairment applied on data from ADNI Hippocampus 19 (6) 579ndash587

Convit A De Leon M Tarshish C De Santi S Tsui W Rusinek H et al 1997 Speci1047297chippocampal volume reductions in individuals at risk for Alzheimers diseaseNeurobiol Aging 18 (2) 131ndash138

Das S Avants B Pluta J Wang H Suh J Weiner M et al 2012 Measuring longitudi-nal change in the hippocampal formation from in vivo high-resolution T2-weightedMRI NeuroImage 60 (2) 1266ndash1279

De Toleto-Morrell L Goncharova I Dickerson B Wilson R Bennett D 2000 Fromhealthy aging to early Alzheimerrsquos disease in vivo detection of entorhinal cortexatrophy Ann N Y Acad Sci 911 240ndash253

DeLong E D eLong D Clarke-Pearson D 1988 Comparing the areas under two or morecorrelated receiver operating characteristic curves a nonparametric approachBiometrics 837ndash845

Dempster ALairdN Rubin D 1977 Maximumlikelihood from incomplete data via theEM algorithm J R Stat Soc 39 (1) 1ndash38

den Heijer T Geerlings M Hoebeek F Hofman A Koudstaal P Breteler M 2006Use of hippocampal and amygdalar volumes on magnetic resonance imagingto predict dementia in cognitively intact elderly people Arch Gen Psychiatry

63 (1) 57ndash62DuA SchuffN Amend DLaakso MHsu YJagust Wet al2001 Magneticresonanceimagingof the entorhinal cortex and hippocampus in mildcognitive impairment andAlzheimers disease J Neurol Neurosurg Psychiatry 71 (4) 441ndash447

Duvernoy H 1988 The Human Hippocampus An Atlas of Applied Anatomy JFBergmann Verlag Munich

EldridgeL KnowltonB Furmanski CBookheimer SEngelS et al 2000 Rememberingepisodes a selective role for the hippocampus during retrieval Nature 3 1149ndash1152

Fischl B 2012 FreeSurfer NeuroImage 62 (2) 774ndash781Fischl BSalat D Busa EAlbert MDieterich MHaselgrove Cet al 2002 Whole brain

segmentation automated labeling of neuroanatomical structures in the human brainNeuron 33 (3) 341ndash355

Fischl B Stevens AA Rajendran N Yeo BT Greve DN Van Leemput K et al 2009Predicting the location of entorhinal cortex from MRI Neuroimage 47 (1) 8ndash17

Fisher RA 1936 The use of multiple measurements in taxonomic problems AnnEugen7 (2) 179ndash188

Frisoni G Laakso M Beltramello A Geroldi C Bianchetti A Soininen H et al 1999Hippocampal and entorhinal cortex atrophy in frontotemporal dementia andAlzheimers disease Neurology 52 (1) 91

Frisoni G Ganzola R Canu E Ruumlb U Pizzini F Alessandrini F et al 2008 Mappinglocal hippocampal changes in Alzheimers disease and normal ageing with MRI at 3Tesla Brain 131 (12) 3266ndash3276

GabrieliJ Brewer JDesmondJ Glover G 1997 Separate neural bases of twofundamentalmemory processes in the human medial temporal lobe Science 276 (5310) 264ndash266

Green RC Mesulam M 1988 Acetylcholinesterase 1047297ber staining in the human hippo-campus and parahippocampal gyrus J Comp Neurol 273 (4) 488ndash499

Harding A Halliday G Kril J 1998 Variation in hippocampal neuron number with ageand brain volume Cereb Cortex 8 (8) 710ndash718

HunsakerM Lee BKesnerR 2008 Evaluating the temporal context of episodic memorythe role of CA3 and CA1 Behav Brain Res 188 (2) 310ndash315

Iglesias J Sabuncu M Van Leemput K 2013 Improved inference in Bayesian segmen-tation using Monte Carlo sampling application to hippocampal sub1047297eld volumetryMed Image Anal 17 (7) 766ndash778

Iglesias JE Sabuncu MR Aganj I Bhatt P Casillas C Salat D et al 2015 An algo-rithm for optimal fusion of atlases with different labeling protocols NeuroImage106 451ndash463

Insausti R Amaral D 2011 Hippocampal formation In Mai J Paxinos G (Eds) HumNerv Syst 896ndash942

Jack C Pe tersen R Xu Y OBrien P Smith G Ivnik R et al 1999 Prediction of ADwith MRI-based hippocampal volume in mild cognitive impairment Neurology 52(7) 1397ndash1403

Kerchner G Hess C Hammond-Rosenbluth K Xu D Rabinovici G Kelley D et al2010 Hippocampal CA1 apical neuropil atrophy in mild Alzheimer disease visualizedwith 7-T MRI Neurology 75 (15) 567ndash576

Kerchner G Deutsch G Zeineh M Dougherty R Saranathan M Rutt B 2012Hippocampal CA1 apical neuropil atrophy and memory performance in Alzheimersdisease NeuroImage 63 (1) 194ndash202

Kesner R 2007 A behavioral analysis of dentate gyrus function Prog Brain Res 163567ndash576

Kesner R 2013 An analysis of the dentate gyrus function Behav Brain Res 254 1ndash7Knierim J Lee I Hargreaves E 2006 Hippocampal place cells parallel input streams

subregional processing and implications for episodic memory Hippocampus 16(9) 755ndash764

Laakso M Soininen H Partanen K Lehtovirta M Hallikainen M Haumlnninen T et al1998 MRI of the hippocampus in Alzheimers disease sensitivity speci1047297city andanalysis of the incorrectly classi1047297ed subjects Neurobiol Aging 19 (1) 23ndash31

Lorente de No R 1934 Studies on the structure of the cerebral cortex II Continuation of the study of the ammonic system J Psychol Neurol 46 113ndash177

Magnain C Augustinack J Reuter M Wachinger C Frosch M Ragan T et al 2014Blockface histology with optical coherence tomography a comparison with Nissistaining NeuroImage 84 (1) 524ndash533

Meng X Rubin D 1993 Maximum likelihood estimation via the ECM algorithm ageneral framework Biometrika 80 (2) 267ndash278

Mueller S Stables L Du A Schuff N Truran D Cashdollar N et al 2007 Measure-ment of hippocampal sub1047297elds and age-related changes with high resolution MRIat 4 T Neurobiol Aging 28 (5) 719

Mueller S Schuff N Yaffe K Madison C Miller B Weiner M 2010 Hippocampalatrophy patterns in mild cognitive impairment and Alzheimers disease Hum BrainMapp 31 (9) 1339ndash1347

Mueller S Yushkevich P Wang L Van Leemput K Mezher A Iglesias J et al2013 Collaboration for a systematic comparison of different techniques tomeasure sub1047297eld volumes announcement and 1047297rst results Alzheimers Dement9 (4) 51

Petersen R Jack C Xu Y Waring S OBrien P Smith GI et al 2000 Memory andMRI-based hippocampal volumes in aging and AD Neurology 54 (3) 581ndash587




Pluta J Yushkevich P Das S Wolk D 2012 In vivo analysis of hippocampal sub1047297eldatrophy in mild cognitive impairment via semi-automatic segmentation of T2-weighted MRI J Alzheimers Dis 31 (1) 85ndash99

Provost S 1990 Estimators for the parameters of a multivariate normal random vectorwith incomplete data on two subvectors and test of independence Comput StatData Anal 9 (1) 37ndash46

Puonti O Iglesias J Van Leemput K 2013 Fast sequence adaptive parcellation of brainmr using parametric models Proc MICCAI 1 727ndash734

Reagh ZM Watabe J Ly M Murray E Yassa MA 2014 Dissociated signals in humandentate gyrus and CA3 predict different facets of recognition memory J Neurosci 34(40) 13301ndash13313

Rolls E 2010 A computational theory of episodic memory formation in the hippocam-pus Behav Brain Res 215 (2) 180ndash196Rosene D Van Hoesen G 1987 The hippocampal formation of the primate brain a

review of some comparative aspects of cytoarchitecture and connections In JonesE Peters A (Eds) Cerebral Cortex vol 6 Plenum Press New York pp 345ndash455

Schmidt B Marrone D Markus E 2012 Disambiguating the similar the dentate gyrusand pattern separation Behav Brain Res 226 (1) 56ndash65

Schoene-Bake J KellerS NiehusmannP Volmering E Elger C Deppe M et al2014In vivo mapping of hippocampal sub1047297elds in mesial temporal l obe epilepsy relationto histopathology Hum Brain Mapp 35 (9) 4718ndash4728

Scoville W Milner B 1957 Loss of recent memory after bilateral hippocampal lesions J Neurol Neurosurg Psychiatry 20 (1) 11

Simic G Kostovic I Winblad B Bogdanovic N 1997 Volume and number of neuronsof the human hippocampal formation in normal aging and Alzheimers diseasae

J Comp Neurol 379 482ndash494Small S Schobel S Buxton R Witter M Barnes C 2011 A pathophysiological frame-

work of hippocampal dysfunction in ageing and disease Nat Rev Neurosci 12 (10)585ndash601

Teicher M Anderson C Polcari A 2012 Childhood maltreatment is associated with

reduced volume in the hippocampal sub1047297elds CA3 dentate gyrus and subiculumProc Natl Acad Sci 109 (9) E563ndashE572

Thal D Rub U Schultz C Sassin I Ghebremedhin E Del Tredici K et al 2000Sequence of A-beta protein deposition in the human medial temporal lobe

J Neuropathol Exp Neurol 59 (8) 733ndash748Van Leemput K 2009 Encoding probabilistic brain atlases using bayesian inference

Med Imaging IEEE Trans 28 (6) 822ndash837

Van Leemput K Maes F Vandereulen D Suetens P 2003 A unifying framework forpartial volume segmentation of brain MR images IEEE Trans Med Imaging 22 (1)105ndash119

Van Leemput K Bakkour A Benner T Wiggins G Wald L Augustinack J et al 2009Automated segmentation of hippocampal sub1047297eldsfrom ultra-high resolution in vivoMRI Hippocampus 19 (6) 549ndash557

Wang L Swanka J Glicka E Gado M Miller M Morris J et al 2003 Changes inhippocampal volume and shape across time distinguish dementia of the Alzheimertype from healthy aging NeuroImage 20 (2) 667ndash682

Wang L Khan A Csernansky J Fischl B Miller M Morris J et al 2009 Fully-automated multi-stage hippocampus mapping in very mild Alzheimer Disease

Hippocampus 19 541ndash548Winterburn J Pruessner J Chavez S Schira M Lobaugh N Voineskos A et al 2013A novel in vivo atlas of human hippocampal sub1047297elds using high-resolution 3 Tmagnetic resonance imaging NeuroImage 74 254ndash265

Wisse L Gerritsen L Zwanenburg J Kiujf H Luijten P Biessels G et al 2012 Sub-1047297elds of the hippocampal formation at 7 T MRI in vivo volumetric assessmentNeuroImage 61 (4) 1043ndash1049

Wisse L Biessels G Heringa S Kuijf H Koek D Luijten P et al 2014 Hippocampalsub1047297eld volumes at 7 T in early Alzheimers disease and normal aging NeurobiolAging 35 (9) 2039ndash2045

Yassa MA Stark CE 2011 Pattern separation in the hippocampus Trends Neurosci 34(10) 515ndash525

Yushkevich P Amaral R Augustinack JC Bender AR Bernstein JD Boccardi M etal 2015 Quantitative Comparison of 21 Protocols for Labeling Hippocampal Sub-1047297elds and Parahippocampal Subregions in In Vivo MRI Towards a Harmonized Seg-mentation Protocol NeuroImage (in press)

Yushkevich PA Pluta JB Wang H Xie L Ding S-L Gertje EC et al 2015 Automat-ed volumetry and regional thickness analysis of hippocampal sub1047297elds and medialtemporal cortical structures in mild cognitive impairment Hum Brain Mapp 36

(1) 258ndash287Yushkevich P Avants B Pluta J Das S Minkoff D Mechanic-Hamilton D et al 2009

A high-resolution computational atlas of the human hippocampus from postmortemmagnetic resonance imaging at 94 Tesla NeuroImage 44 (2) 385

Yushkevich P Wang H Pluta J Das S Craige C Avants B et al 2010 Nearly auto-matic segmentation of hippocampal sub1047297elds in in vivo focal T2-weighted MRINeuroImage 53 (4) 1208ndash1224




Introduction

The hippocampal formation is a brain region with a critical role in

declarative and episodic memory (Scoville and Milner 1957 Eldridge

et al 2000) as well as a focus of structural change in normal aging

(Petersen et al 2000 Frisoni et al 2008) and diseases such as epilepsy

(Cendes et al 1993) and most notably Alzheimers disease (AD)

(Laakso et al 1998 Du et al 2001 Apostolova et al 2006) The hippo-

campal formation consists of a number of distinct interacting subre-gions which comprise a complex heterogeneous structure Despite its

internal complexity limits in MRI resolution have traditionally forced

researchers to model the hippocampus as a single homogeneous struc-

ture in neuroimaging studies of aging and AD (Boccardi et al 2011

Chupin et al 2009) Even though these studies have shown that

whole hippocampal volumes derived from automatically or manually

segmented MRI scans are powerful biomarkers for AD ( Convit et al

1997 Jack et al 1999 Frisoni et al 1999 De Toleto-Morrell et al

2000 den Heijer et al 2006 Wang et al 2003 Fischl et al 2002 )

treating the hippocampus as a single entity disregards potentially useful

information about its subregions In animal studies these subregions

have been shown to have different memory functions ( Acsaacutedy and

Kaacuteli 2007 Hunsaker et al 2008 Kesner 2007 Rolls 2010 Schmidt

et al 2012) In humans they are also thought to play different roles in

memory and learning (Gabrieli et al 1997 Acsaacutedy and Kaacuteli 2007

Knierim et al 2006 Kesner 2013 Kesner 2007 Reagh et al 2014

Yassa and Stark 2011) and to be affected differently by AD and normal

aging mdash as indicated by ex vivo histological studies (Braak and Braak

1991 Braak and Braak 1997 Arnold et al 1991 Thal et al 2000

Brady and Mufson 1991 Simic et al 1997 Harding et al 1998)

Findings from histological studies on hippocampal samples have

sparked interest in studying the hippocampal subregions in vivo with

MRI which has been made possible by recent advances in MRI acquisi-

tion Neuroimaging studies that have characterized the subregions in

normal aging and AD with in vivo MRI include (Mueller et al 2007

Wang et al 2009 Mueller et al 2010 Small et al 2011 Kerchner

et al 2012 Wisse et al 2012 2014 Burggren et al 2008) Most of

these studies rely on manual segmentations made on T2-weighted MRI

data of thehippocampalformation TheT2 imagesare often acquiredan-isotropically such that resolution along the direction of the major axis of

the hippocampus is reduced in exchange for higher in-plane resolution

within each coronal slice This design choice is motivated by the internal

structure of the hippocampus resembling a Swiss roll its spiral structure

changes less rapidly along its major axis which is almost parallel to the

anteriorndashposterior direction In in vivo T2-weighted data part of this spi-

ral becomes visible as a hypointense band that corresponds to the stra-

tum radiatum lacunosum moleculare hippocampal sulcus and

molecular layer of the dentate gyrus These layers separate the hippo-

campus from the dentate gyrus Henceforth for simplicity in writing

we will refer to this band as the ldquomolecular layerrdquo2

Manual segmentation protocols of high resolution in vivo MRI data

of the hippocampal sub1047297elds3 often rely heavily on this molecular

layer which is the most prominent feature of the internal region of the hippocampus that is visible in MRI However manual delineation

of the subregions in these high-resolution images is extremely labor-

intensivemdash approximately 50 hoursper caseFew laboratories currently

possess the resources in neuroanatomical expertise and staf 1047297ng that

are required to carry out such studies Even within those laboratories

the number of cases that can be used in a study is limited by how

time-consuming manually tracing the subregions is which in turns

limits the statistical power of the analysis

These limitations can be overcome with the use of automated

algorithms Two major methods have been proposed for automated

and semi-automated hippocampal subregion segmentation so far In

(Yushkevich et al 2010) ndash further validated in (Pluta et al 2012) ndash

Yushkevich and colleagues combined multi-atlas segmentation similarity-

weighted voting and a learning-based label bias correction technique to

estimate the subregion segmentation in a nearly automated fashionThe user needed to provide an initial partitioning of MRI slices into hip-

pocampal head body and tail (this requirement was dropped in their

recent study Yushkevich et al 2015) In (Van Leemput et al 2009)

our group introduced a fully automated method based on a statistical

atlas of hippocampal anatomy and a generative model of MRI data

These two methods approach the segmentation problem from dif-

ferent perspectives mdash parametric and non-parametric The algorithm

we developed ndash which follows a generative parametric approach ndash

focuses on modeling the spatial distribution of the hippocampal

subregions and surrounding brain structures (ie the underlying

segmentation) which is learned from labeled training data The seg-

mentation which is a hidden variable in the model is connected to

the observed image data through a generative process of image formation

that does notmake any assumptionsabouttheMRI acquisitionThisisindeed

the strongest point of the algorithm since it makes it adaptive to any MRI

pulse sequence and resolution that might have been used to acquire the

datamdasheven if multimodal (Puontiet al 2013) Converselythealgorithmde-

veloped by Yushkevich and co-workers relies on a combination of a

registration-based multi-atlas algorithm (a non-parametric method) and

machine learning techniques Both components of their method effectively

exploit prior knowledge about the distribution of image intensities derived

from training data mdash information which our parametric method disregards

Whilethe useof priorknowledgeaboutthe image intensitiesis advantageous

when the MRI pulse sequence of the test scan matches that of the training

data segmentation of MRI images with different contrast properties is not

possible with such an approach Nonetheless both Yushkevichs method

and ours have successfully been used to carry out subregion studies on

large populations (Teicher et al 2012 Das et al 2012 Iglesias et al 2013)

Our original sub1047297eld segmentation method which is publicly availableas part of the FreeSurfer open-source software package (Fischl FreeSurfer

2012) (version 53) is based on a probabilistic atlas that was built from

in vivo MRI data acquired at 038 times 038 times 08 mm resolution (Van

Leemput et al 2009) Henceforth we refer to this atlas as the ldquoin vivo

atlasrdquo (FreeSurfer v53) The resolution of this atlas is only suf 1047297cient to pro-

duce a coarse segmentation of the subregions in standard-resolution MRI

(ie 1 mm) a more accurate model of anatomy is necessary to analyze

newer higher resolution data where the hippocampal substructures are

more clearly visualized Speci1047297cally the in vivo atlas in FreeSurfer v53 suf-

fersfromthree shortcomings First the image resolution of the in vivo train-

ing data was insuf 1047297cient for the human labelers to completely distinguish

the subregions forcing them to heavily rely on geometric criteria to trace

boundaries which affected the accuracy of their annotations In particular

a problematic consequence is that the molecular layer was not labeledcompromising the ability of the atlas to segment high-resolution in vivo

data A second issue is that the delineation protocol was designed for the

hippocampal body and did not translate well to the hippocampal head or

tail Due to the second issue a third problem is that the volumes of the sub-

regions did not agreewell with those from histological studies (Simic et al

1997 Harding et al 1998) as pointed out by (Schoene-Bake et al 2014)

In this studywe address these shortcomings by replacingthe hippo-

campal atlas in FreeSurfer v53 with a new version (FreeSurfer v60)

built with a novel atlasing algorithm and ex vivo MRI data from autopsy

brains Since motion effects are eliminated much longer MRI acquisi-

tions are possible when imaging post-mortem samples Our ex vivo

imaging protocol yields images with extremely high resolution and

signal-to-noise ratio dramatically higher than is possible in vivo

which allows us to accurately identify more subregions with a

2 This band hasbeen referred to as theldquodarkbandrdquo in theliteraturebut is actually bright

when imaged with T1-weighted MRI therefore we prefer to use the term ldquomolecular

layerrdquo3 We use the term ldquosub1047297eldsrdquo to refer to the CA structures (ie CA1ndash4) and subregions

to refer to the whole set of hippocampal substructures including parasubiculum

presubiculumsubiculum1047297mbriamolecularlayer and hippocampusndashamygdala transition

area (in addition to the sub1047297elds)
















































Atlas construction

























































Table 1




























































































atlas in FreeSurfer
















Underlying model




Table 2







Parasubiculum

(yellow)




Presubiculum

(dark purple)












1047297
















gyrus (cyan)











Molecular layer

(brown)



































hippocampus






Fig 4)








K α nk =

1




U xmj xr Keth THORN

β

frac14 exp minus

XT


β

24

35











constant





sumN nfrac141α

knϕ






m

we have that



K




m) (for






pi cmi jα xm

K

frac14X

kisincmi



m) = cim If









probabilities








where α and ^ x m



α ^ x m


n


Keth THORN




fα ^ x m



with


frac14XM

mfrac141


XI

ifrac141

logX

kisincm

i


8lt

9=
















1

β

XT

t frac141


part xm thorn

XI

ifrac141

XkisinC mi


part xmXkisinC mi


frac14 minus1

β

XT

t frac141


part xm thorn

XI

ifrac141

XkisinC mi

XN


n xieth THORN

part xmXkisinC mi

XN

nfrac141α knϕ

mn xieth THORN





x

m







mfrac141

XI

ifrac141

XN

nfrac141

Xk

W mkin log αk


i

h iminusW mk

in log W mkin

leXM

mfrac141

XI

ifrac141

logX

k

XN

nfrac141


i

frac14XM

mfrac141

XI

ifrac141

logX

kisincm

i



W mkin frac14

~αknϕ


i

X

n0

Xk

0 ~αk0


0isincmi

eth4THORN


(M step)

αkn frac14

XM

mfrac141

XI

ifrac141W mk

inXM

m0frac141

XI

i0frac141

Xk

0 W m0k

0

i0n

eth5THORN



















pi lmi jα xm

K

by pi cmi jα xm

K





Z prod

N

nfrac141N n thorn 1


prod

M


m K

eth6THORN


I ifrac141W mk

in α ^ xm













Data preprocessing































ability





4




























































Generative model























Table 3





Ex vivo atlas 786 51 254 337 520 179 211 244 465 466 50 92 320


UPenn NA 1574 86 201 167 127

Simica

802 404 591 139 197 59Harding 69 321 529 731 138 169 50










ifrac141


frac14 prod

I

ifrac141



ΣG










p μ G

ΣGf g







obtained)












^ L frac14 argmaxL


asymp argmaxL

p L j^ x ^ μ G

ΣG

n o Y α xr

β K


^ x ^ μ G

ΣG


x μ Gf g ΣGf g

p x μ G

ΣGf gjY α xr

β K

eth7THORN



^ x ^ μ G

ΣG


x μ Gf g Σ Gf g

p Y jα x K μ G

ΣGf g

p xj β xr

Keth THORN p μ G

ΣGf g

frac14



XI

ifrac141 log


h ithorn

XG


eth8THORN








ΩGi frac14




XI

ifrac141ΩGi y i

ν G thornXI

ifrac141ΩG

i

ΣGlarr

XI

ifrac141ΩG


XI

ifrac141ΩG

i


ΣG



p L j^ x ^ μ G

ΣG

n o


li asymp argmaxk



V k frac14XI

ifrac141



Xk


pi k0jα x K

eth9THORN


hyperparameters































interpolation















































































































































































































































6


Table 4








LR average

(Yushkevich et al)


Parasubiculum 015 73 027 022 134 019

Presubiculum 021 121 020 008 41 040

Subiculum 014 66 029 018 95 023 25 057 59 027

CA1 003 24 058 002 18 069 11 095 10 (CA123) 099

CA23 002 18 071 010 47 036 27 (CA12) 055

CA4 003 23 059 004 25 057 26 (CA4DG) 042


Molec layer 002 20 067 005 28 052

Fimbria 002 19 068 004 26 055

Hippo 1047297ssure 045 N1000 010 026 187 017

HATA 020 111 021 007 36 043

Hippo tail 045 N1000 010 049 N1000 010

Whole hippo 004 27 054 004 25 056


Perirhinal 223 010

Table 5




Left T1 010 047 023 008 012 008 011 009 004 030 030 044 008

T1 + T2 015 021 014 003 002 003 002 002 002 045 020 045 004

Right T1 034 047 032 010 025 008 006 012 007 035 021 028 010

T1 + T2 022 008 018 002 010 004 001 005 004 026 007 049 004



















































































Table 6



the two groups





Subiculum 189 178 189 154

CA1 199 090 182 067

CA23 158 139 159 124

CA4 179 153 180



Fimbria 060 070 039 067


HATA 145 151

























































































Table 7


Atlas Accuracy

at elbow

AUROC


Whole hippocampus


840 0901
























































Acknowledgments





















Sub1047297

eld Volumetryrdquo














































XI

ifrac141ΩG

i ~ y i

ν G thornXI

ifrac141ΩG

i




o ieth THORNG


o ieth THORNG


ΣGlarr

XI

ifrac141ΩG


t thorn ~Ψi


XI

ifrac141

ΩG

i






i frac14 0 and ~Ψm


mo ieth THORNG Σ

o ieth THORNG

h iminus1

Σmo ieth THORNG




pi y ij μ GΣG

frac14 N y o

i μo ieth THORN


h i











References







































































































































Atlas construction

























































Table 1




























































































atlas in FreeSurfer
















Underlying model




Table 2







Parasubiculum

(yellow)




Presubiculum

(dark purple)












1047297
















gyrus (cyan)











Molecular layer

(brown)



































hippocampus






Fig 4)








K α nk =

1




U xmj xr Keth THORN

β

frac14 exp minus

XT


β

24

35











constant





sumN nfrac141α

knϕ






m

we have that



K




m) (for






pi cmi jα xm

K

frac14X

kisincmi



m) = cim If









probabilities








where α and ^ x m



α ^ x m


n


Keth THORN




fα ^ x m



with


frac14XM

mfrac141


XI

ifrac141

logX

kisincm

i


8lt

9=
















1

β

XT

t frac141


part xm thorn

XI

ifrac141

XkisinC mi


part xmXkisinC mi


frac14 minus1

β

XT

t frac141


part xm thorn

XI

ifrac141

XkisinC mi

XN


n xieth THORN

part xmXkisinC mi

XN

nfrac141α knϕ

mn xieth THORN





x

m







mfrac141

XI

ifrac141

XN

nfrac141

Xk

W mkin log αk


i

h iminusW mk

in log W mkin

leXM

mfrac141

XI

ifrac141

logX

k

XN

nfrac141


i

frac14XM

mfrac141

XI

ifrac141

logX

kisincm

i



W mkin frac14

~αknϕ


i

X

n0

Xk

0 ~αk0


0isincmi

eth4THORN


(M step)

αkn frac14

XM

mfrac141

XI

ifrac141W mk

inXM

m0frac141

XI

i0frac141

Xk

0 W m0k

0

i0n

eth5THORN



















pi lmi jα xm

K

by pi cmi jα xm

K





Z prod

N

nfrac141N n thorn 1


prod

M


m K

eth6THORN


I ifrac141W mk

in α ^ xm













Data preprocessing































ability





4




























































Generative model























Table 3





Ex vivo atlas 786 51 254 337 520 179 211 244 465 466 50 92 320


UPenn NA 1574 86 201 167 127

Simica

802 404 591 139 197 59Harding 69 321 529 731 138 169 50










ifrac141


frac14 prod

I

ifrac141



ΣG










p μ G

ΣGf g







obtained)












^ L frac14 argmaxL


asymp argmaxL

p L j^ x ^ μ G

ΣG

n o Y α xr

β K


^ x ^ μ G

ΣG


x μ Gf g ΣGf g

p x μ G

ΣGf gjY α xr

β K

eth7THORN



^ x ^ μ G

ΣG


x μ Gf g Σ Gf g

p Y jα x K μ G

ΣGf g

p xj β xr

Keth THORN p μ G

ΣGf g

frac14



XI

ifrac141 log


h ithorn

XG


eth8THORN








ΩGi frac14




XI

ifrac141ΩGi y i

ν G thornXI

ifrac141ΩG

i

ΣGlarr

XI

ifrac141ΩG


XI

ifrac141ΩG

i


ΣG



p L j^ x ^ μ G

ΣG

n o


li asymp argmaxk



V k frac14XI

ifrac141



Xk


pi k0jα x K

eth9THORN


hyperparameters































interpolation















































































































































































































































6


Table 4








LR average

(Yushkevich et al)


Parasubiculum 015 73 027 022 134 019

Presubiculum 021 121 020 008 41 040

Subiculum 014 66 029 018 95 023 25 057 59 027

CA1 003 24 058 002 18 069 11 095 10 (CA123) 099

CA23 002 18 071 010 47 036 27 (CA12) 055

CA4 003 23 059 004 25 057 26 (CA4DG) 042


Molec layer 002 20 067 005 28 052

Fimbria 002 19 068 004 26 055

Hippo 1047297ssure 045 N1000 010 026 187 017

HATA 020 111 021 007 36 043

Hippo tail 045 N1000 010 049 N1000 010

Whole hippo 004 27 054 004 25 056


Perirhinal 223 010

Table 5




Left T1 010 047 023 008 012 008 011 009 004 030 030 044 008

T1 + T2 015 021 014 003 002 003 002 002 002 045 020 045 004

Right T1 034 047 032 010 025 008 006 012 007 035 021 028 010

T1 + T2 022 008 018 002 010 004 001 005 004 026 007 049 004



















































































Table 6



the two groups





Subiculum 189 178 189 154

CA1 199 090 182 067

CA23 158 139 159 124

CA4 179 153 180



Fimbria 060 070 039 067


HATA 145 151

























































































Table 7


Atlas Accuracy

at elbow

AUROC


Whole hippocampus


840 0901
























































Acknowledgments





















Sub1047297

eld Volumetryrdquo














































XI

ifrac141ΩG

i ~ y i

ν G thornXI

ifrac141ΩG

i




o ieth THORNG


o ieth THORNG


ΣGlarr

XI

ifrac141ΩG


t thorn ~Ψi


XI

ifrac141

ΩG

i






i frac14 0 and ~Ψm


mo ieth THORNG Σ

o ieth THORNG

h iminus1

Σmo ieth THORNG




pi y ij μ GΣG

frac14 N y o

i μo ieth THORN


h i











References
































































































































































atlas in FreeSurfer
















Underlying model




Table 2







Parasubiculum

(yellow)




Presubiculum

(dark purple)












1047297
















gyrus (cyan)











Molecular layer

(brown)



































hippocampus






Fig 4)








K α nk =

1




U xmj xr Keth THORN

β

frac14 exp minus

XT


β

24

35











constant





sumN nfrac141α

knϕ






m

we have that



K




m) (for






pi cmi jα xm

K

frac14X

kisincmi



m) = cim If









probabilities








where α and ^ x m



α ^ x m


n


Keth THORN




fα ^ x m



with


frac14XM

mfrac141


XI

ifrac141

logX

kisincm

i


8lt

9=
















1

β

XT

t frac141


part xm thorn

XI

ifrac141

XkisinC mi


part xmXkisinC mi


frac14 minus1

β

XT

t frac141


part xm thorn

XI

ifrac141

XkisinC mi

XN


n xieth THORN

part xmXkisinC mi

XN

nfrac141α knϕ

mn xieth THORN





x

m







mfrac141

XI

ifrac141

XN

nfrac141

Xk

W mkin log αk


i

h iminusW mk

in log W mkin

leXM

mfrac141

XI

ifrac141

logX

k

XN

nfrac141


i

frac14XM

mfrac141

XI

ifrac141

logX

kisincm

i



W mkin frac14

~αknϕ


i

X

n0

Xk

0 ~αk0


0isincmi

eth4THORN


(M step)

αkn frac14

XM

mfrac141

XI

ifrac141W mk

inXM

m0frac141

XI

i0frac141

Xk

0 W m0k

0

i0n

eth5THORN



















pi lmi jα xm

K

by pi cmi jα xm

K





Z prod

N

nfrac141N n thorn 1


prod

M


m K

eth6THORN


I ifrac141W mk

in α ^ xm













Data preprocessing































ability





4




























































Generative model























Table 3





Ex vivo atlas 786 51 254 337 520 179 211 244 465 466 50 92 320


UPenn NA 1574 86 201 167 127

Simica

802 404 591 139 197 59Harding 69 321 529 731 138 169 50










ifrac141


frac14 prod

I

ifrac141



ΣG










p μ G

ΣGf g







obtained)












^ L frac14 argmaxL


asymp argmaxL

p L j^ x ^ μ G

ΣG

n o Y α xr

β K


^ x ^ μ G

ΣG


x μ Gf g ΣGf g

p x μ G

ΣGf gjY α xr

β K

eth7THORN



^ x ^ μ G

ΣG


x μ Gf g Σ Gf g

p Y jα x K μ G

ΣGf g

p xj β xr

Keth THORN p μ G

ΣGf g

frac14



XI

ifrac141 log


h ithorn

XG


eth8THORN








ΩGi frac14




XI

ifrac141ΩGi y i

ν G thornXI

ifrac141ΩG

i

ΣGlarr

XI

ifrac141ΩG


XI

ifrac141ΩG

i


ΣG



p L j^ x ^ μ G

ΣG

n o


li asymp argmaxk



V k frac14XI

ifrac141



Xk


pi k0jα x K

eth9THORN


hyperparameters































interpolation















































































































































































































































6


Table 4








LR average

(Yushkevich et al)


Parasubiculum 015 73 027 022 134 019

Presubiculum 021 121 020 008 41 040

Subiculum 014 66 029 018 95 023 25 057 59 027

CA1 003 24 058 002 18 069 11 095 10 (CA123) 099

CA23 002 18 071 010 47 036 27 (CA12) 055

CA4 003 23 059 004 25 057 26 (CA4DG) 042


Molec layer 002 20 067 005 28 052

Fimbria 002 19 068 004 26 055

Hippo 1047297ssure 045 N1000 010 026 187 017

HATA 020 111 021 007 36 043

Hippo tail 045 N1000 010 049 N1000 010

Whole hippo 004 27 054 004 25 056


Perirhinal 223 010

Table 5




Left T1 010 047 023 008 012 008 011 009 004 030 030 044 008

T1 + T2 015 021 014 003 002 003 002 002 002 045 020 045 004

Right T1 034 047 032 010 025 008 006 012 007 035 021 028 010

T1 + T2 022 008 018 002 010 004 001 005 004 026 007 049 004



















































































Table 6



the two groups





Subiculum 189 178 189 154

CA1 199 090 182 067

CA23 158 139 159 124

CA4 179 153 180



Fimbria 060 070 039 067


HATA 145 151

























































































Table 7


Atlas Accuracy

at elbow

AUROC


Whole hippocampus


840 0901
























































Acknowledgments





















Sub1047297

eld Volumetryrdquo














































XI

ifrac141ΩG

i ~ y i

ν G thornXI

ifrac141ΩG

i




o ieth THORNG


o ieth THORNG


ΣGlarr

XI

ifrac141ΩG


t thorn ~Ψi


XI

ifrac141

ΩG

i






i frac14 0 and ~Ψm


mo ieth THORNG Σ

o ieth THORNG

h iminus1

Σmo ieth THORNG




pi y ij μ GΣG

frac14 N y o

i μo ieth THORN


h i











References





































































































Underlying model




Table 2







Parasubiculum

(yellow)




Presubiculum

(dark purple)












1047297
















gyrus (cyan)











Molecular layer

(brown)



































hippocampus






Fig 4)








K α nk =

1




U xmj xr Keth THORN

β

frac14 exp minus

XT


β

24

35











constant





sumN nfrac141α

knϕ






m

we have that



K




m) (for






pi cmi jα xm

K

frac14X

kisincmi



m) = cim If









probabilities








where α and ^ x m



α ^ x m


n


Keth THORN




fα ^ x m



with


frac14XM

mfrac141


XI

ifrac141

logX

kisincm

i


8lt

9=
















1

β

XT

t frac141


part xm thorn

XI

ifrac141

XkisinC mi


part xmXkisinC mi


frac14 minus1

β

XT

t frac141


part xm thorn

XI

ifrac141

XkisinC mi

XN


n xieth THORN

part xmXkisinC mi

XN

nfrac141α knϕ

mn xieth THORN





x

m







mfrac141

XI

ifrac141

XN

nfrac141

Xk

W mkin log αk


i

h iminusW mk

in log W mkin

leXM

mfrac141

XI

ifrac141

logX

k

XN

nfrac141


i

frac14XM

mfrac141

XI

ifrac141

logX

kisincm

i



W mkin frac14

~αknϕ


i

X

n0

Xk

0 ~αk0


0isincmi

eth4THORN


(M step)

αkn frac14

XM

mfrac141

XI

ifrac141W mk

inXM

m0frac141

XI

i0frac141

Xk

0 W m0k

0

i0n

eth5THORN



















pi lmi jα xm

K

by pi cmi jα xm

K





Z prod

N

nfrac141N n thorn 1


prod

M


m K

eth6THORN


I ifrac141W mk

in α ^ xm













Data preprocessing































ability





4




























































Generative model























Table 3





Ex vivo atlas 786 51 254 337 520 179 211 244 465 466 50 92 320


UPenn NA 1574 86 201 167 127

Simica

802 404 591 139 197 59Harding 69 321 529 731 138 169 50










ifrac141


frac14 prod

I

ifrac141



ΣG










p μ G

ΣGf g







obtained)












^ L frac14 argmaxL


asymp argmaxL

p L j^ x ^ μ G

ΣG

n o Y α xr

β K


^ x ^ μ G

ΣG


x μ Gf g ΣGf g

p x μ G

ΣGf gjY α xr

β K

eth7THORN



^ x ^ μ G

ΣG


x μ Gf g Σ Gf g

p Y jα x K μ G

ΣGf g

p xj β xr

Keth THORN p μ G

ΣGf g

frac14



XI

ifrac141 log


h ithorn

XG


eth8THORN








ΩGi frac14




XI

ifrac141ΩGi y i

ν G thornXI

ifrac141ΩG

i

ΣGlarr

XI

ifrac141ΩG


XI

ifrac141ΩG

i


ΣG



p L j^ x ^ μ G

ΣG

n o


li asymp argmaxk



V k frac14XI

ifrac141



Xk


pi k0jα x K

eth9THORN


hyperparameters































interpolation















































































































































































































































6


Table 4








LR average

(Yushkevich et al)


Parasubiculum 015 73 027 022 134 019

Presubiculum 021 121 020 008 41 040

Subiculum 014 66 029 018 95 023 25 057 59 027

CA1 003 24 058 002 18 069 11 095 10 (CA123) 099

CA23 002 18 071 010 47 036 27 (CA12) 055

CA4 003 23 059 004 25 057 26 (CA4DG) 042


Molec layer 002 20 067 005 28 052

Fimbria 002 19 068 004 26 055

Hippo 1047297ssure 045 N1000 010 026 187 017

HATA 020 111 021 007 36 043

Hippo tail 045 N1000 010 049 N1000 010

Whole hippo 004 27 054 004 25 056


Perirhinal 223 010

Table 5




Left T1 010 047 023 008 012 008 011 009 004 030 030 044 008

T1 + T2 015 021 014 003 002 003 002 002 002 045 020 045 004

Right T1 034 047 032 010 025 008 006 012 007 035 021 028 010

T1 + T2 022 008 018 002 010 004 001 005 004 026 007 049 004



















































































Table 6



the two groups





Subiculum 189 178 189 154

CA1 199 090 182 067

CA23 158 139 159 124

CA4 179 153 180



Fimbria 060 070 039 067


HATA 145 151

























































































Table 7


Atlas Accuracy

at elbow

AUROC


Whole hippocampus


840 0901
























































Acknowledgments





















Sub1047297

eld Volumetryrdquo














































XI

ifrac141ΩG

i ~ y i

ν G thornXI

ifrac141ΩG

i




o ieth THORNG


o ieth THORNG


ΣGlarr

XI

ifrac141ΩG


t thorn ~Ψi


XI

ifrac141

ΩG

i






i frac14 0 and ~Ψm


mo ieth THORNG Σ

o ieth THORNG

h iminus1

Σmo ieth THORNG




pi y ij μ GΣG

frac14 N y o

i μo ieth THORN


h i











References

















































































































hippocampus






Fig 4)








K α nk =

1




U xmj xr Keth THORN

β

frac14 exp minus

XT


β

24

35











constant





sumN nfrac141α

knϕ






m

we have that



K




m) (for






pi cmi jα xm

K

frac14X

kisincmi



m) = cim If









probabilities








where α and ^ x m



α ^ x m


n


Keth THORN




fα ^ x m



with


frac14XM

mfrac141


XI

ifrac141

logX

kisincm

i


8lt

9=
















1

β

XT

t frac141


part xm thorn

XI

ifrac141

XkisinC mi


part xmXkisinC mi


frac14 minus1

β

XT

t frac141


part xm thorn

XI

ifrac141

XkisinC mi

XN


n xieth THORN

part xmXkisinC mi

XN

nfrac141α knϕ

mn xieth THORN





x

m







mfrac141

XI

ifrac141

XN

nfrac141

Xk

W mkin log αk


i

h iminusW mk

in log W mkin

leXM

mfrac141

XI

ifrac141

logX

k

XN

nfrac141


i

frac14XM

mfrac141

XI

ifrac141

logX

kisincm

i



W mkin frac14

~αknϕ


i

X

n0

Xk

0 ~αk0


0isincmi

eth4THORN


(M step)

αkn frac14

XM

mfrac141

XI

ifrac141W mk

inXM

m0frac141

XI

i0frac141

Xk

0 W m0k

0

i0n

eth5THORN



















pi lmi jα xm

K

by pi cmi jα xm

K





Z prod

N

nfrac141N n thorn 1


prod

M


m K

eth6THORN


I ifrac141W mk

in α ^ xm













Data preprocessing































ability





4




























































Generative model























Table 3





Ex vivo atlas 786 51 254 337 520 179 211 244 465 466 50 92 320


UPenn NA 1574 86 201 167 127

Simica

802 404 591 139 197 59Harding 69 321 529 731 138 169 50










ifrac141


frac14 prod

I

ifrac141



ΣG










p μ G

ΣGf g







obtained)












^ L frac14 argmaxL


asymp argmaxL

p L j^ x ^ μ G

ΣG

n o Y α xr

β K


^ x ^ μ G

ΣG


x μ Gf g ΣGf g

p x μ G

ΣGf gjY α xr

β K

eth7THORN



^ x ^ μ G

ΣG


x μ Gf g Σ Gf g

p Y jα x K μ G

ΣGf g

p xj β xr

Keth THORN p μ G

ΣGf g

frac14



XI

ifrac141 log


h ithorn

XG


eth8THORN








ΩGi frac14




XI

ifrac141ΩGi y i

ν G thornXI

ifrac141ΩG

i

ΣGlarr

XI

ifrac141ΩG


XI

ifrac141ΩG

i


ΣG



p L j^ x ^ μ G

ΣG

n o


li asymp argmaxk



V k frac14XI

ifrac141



Xk


pi k0jα x K

eth9THORN


hyperparameters































interpolation















































































































































































































































6


Table 4








LR average

(Yushkevich et al)


Parasubiculum 015 73 027 022 134 019

Presubiculum 021 121 020 008 41 040

Subiculum 014 66 029 018 95 023 25 057 59 027

CA1 003 24 058 002 18 069 11 095 10 (CA123) 099

CA23 002 18 071 010 47 036 27 (CA12) 055

CA4 003 23 059 004 25 057 26 (CA4DG) 042


Molec layer 002 20 067 005 28 052

Fimbria 002 19 068 004 26 055

Hippo 1047297ssure 045 N1000 010 026 187 017

HATA 020 111 021 007 36 043

Hippo tail 045 N1000 010 049 N1000 010

Whole hippo 004 27 054 004 25 056


Perirhinal 223 010

Table 5




Left T1 010 047 023 008 012 008 011 009 004 030 030 044 008

T1 + T2 015 021 014 003 002 003 002 002 002 045 020 045 004

Right T1 034 047 032 010 025 008 006 012 007 035 021 028 010

T1 + T2 022 008 018 002 010 004 001 005 004 026 007 049 004



















































































Table 6



the two groups





Subiculum 189 178 189 154

CA1 199 090 182 067

CA23 158 139 159 124

CA4 179 153 180



Fimbria 060 070 039 067


HATA 145 151

























































































Table 7


Atlas Accuracy

at elbow

AUROC


Whole hippocampus


840 0901
























































Acknowledgments





















Sub1047297

eld Volumetryrdquo














































XI

ifrac141ΩG

i ~ y i

ν G thornXI

ifrac141ΩG

i




o ieth THORNG


o ieth THORNG


ΣGlarr

XI

ifrac141ΩG


t thorn ~Ψi


XI

ifrac141

ΩG

i






i frac14 0 and ~Ψm


mo ieth THORNG Σ

o ieth THORNG

h iminus1

Σmo ieth THORNG




pi y ij μ GΣG

frac14 N y o

i μo ieth THORN


h i











References



























































































where α and ^ x m



α ^ x m


n


Keth THORN




fα ^ x m



with


frac14XM

mfrac141


XI

ifrac141

logX

kisincm

i


8lt

9=
















1

β

XT

t frac141


part xm thorn

XI

ifrac141

XkisinC mi


part xmXkisinC mi


frac14 minus1

β

XT

t frac141


part xm thorn

XI

ifrac141

XkisinC mi

XN


n xieth THORN

part xmXkisinC mi

XN

nfrac141α knϕ

mn xieth THORN





x

m







mfrac141

XI

ifrac141

XN

nfrac141

Xk

W mkin log αk


i

h iminusW mk

in log W mkin

leXM

mfrac141

XI

ifrac141

logX

k

XN

nfrac141


i

frac14XM

mfrac141

XI

ifrac141

logX

kisincm

i



W mkin frac14

~αknϕ


i

X

n0

Xk

0 ~αk0


0isincmi

eth4THORN


(M step)

αkn frac14

XM

mfrac141

XI

ifrac141W mk

inXM

m0frac141

XI

i0frac141

Xk

0 W m0k

0

i0n

eth5THORN



















pi lmi jα xm

K

by pi cmi jα xm

K





Z prod

N

nfrac141N n thorn 1


prod

M


m K

eth6THORN


I ifrac141W mk

in α ^ xm













Data preprocessing































ability





4




























































Generative model























Table 3





Ex vivo atlas 786 51 254 337 520 179 211 244 465 466 50 92 320


UPenn NA 1574 86 201 167 127

Simica

802 404 591 139 197 59Harding 69 321 529 731 138 169 50










ifrac141


frac14 prod

I

ifrac141



ΣG










p μ G

ΣGf g







obtained)












^ L frac14 argmaxL


asymp argmaxL

p L j^ x ^ μ G

ΣG

n o Y α xr

β K


^ x ^ μ G

ΣG


x μ Gf g ΣGf g

p x μ G

ΣGf gjY α xr

β K

eth7THORN



^ x ^ μ G

ΣG


x μ Gf g Σ Gf g

p Y jα x K μ G

ΣGf g

p xj β xr

Keth THORN p μ G

ΣGf g

frac14



XI

ifrac141 log


h ithorn

XG


eth8THORN








ΩGi frac14




XI

ifrac141ΩGi y i

ν G thornXI

ifrac141ΩG

i

ΣGlarr

XI

ifrac141ΩG


XI

ifrac141ΩG

i


ΣG



p L j^ x ^ μ G

ΣG

n o


li asymp argmaxk



V k frac14XI

ifrac141



Xk


pi k0jα x K

eth9THORN


hyperparameters































interpolation















































































































































































































































6


Table 4








LR average

(Yushkevich et al)


Parasubiculum 015 73 027 022 134 019

Presubiculum 021 121 020 008 41 040

Subiculum 014 66 029 018 95 023 25 057 59 027

CA1 003 24 058 002 18 069 11 095 10 (CA123) 099

CA23 002 18 071 010 47 036 27 (CA12) 055

CA4 003 23 059 004 25 057 26 (CA4DG) 042


Molec layer 002 20 067 005 28 052

Fimbria 002 19 068 004 26 055

Hippo 1047297ssure 045 N1000 010 026 187 017

HATA 020 111 021 007 36 043

Hippo tail 045 N1000 010 049 N1000 010

Whole hippo 004 27 054 004 25 056


Perirhinal 223 010

Table 5




Left T1 010 047 023 008 012 008 011 009 004 030 030 044 008

T1 + T2 015 021 014 003 002 003 002 002 002 045 020 045 004

Right T1 034 047 032 010 025 008 006 012 007 035 021 028 010

T1 + T2 022 008 018 002 010 004 001 005 004 026 007 049 004



















































































Table 6



the two groups





Subiculum 189 178 189 154

CA1 199 090 182 067

CA23 158 139 159 124

CA4 179 153 180



Fimbria 060 070 039 067


HATA 145 151

























































































Table 7


Atlas Accuracy

at elbow

AUROC


Whole hippocampus


840 0901
























































Acknowledgments





















Sub1047297

eld Volumetryrdquo














































XI

ifrac141ΩG

i ~ y i

ν G thornXI

ifrac141ΩG

i




o ieth THORNG


o ieth THORNG


ΣGlarr

XI

ifrac141ΩG


t thorn ~Ψi


XI

ifrac141

ΩG

i






i frac14 0 and ~Ψm


mo ieth THORNG Σ

o ieth THORNG

h iminus1

Σmo ieth THORNG




pi y ij μ GΣG

frac14 N y o

i μo ieth THORN


h i











References










































































































ability





4




























































Generative model























Table 3





Ex vivo atlas 786 51 254 337 520 179 211 244 465 466 50 92 320


UPenn NA 1574 86 201 167 127

Simica

802 404 591 139 197 59Harding 69 321 529 731 138 169 50










ifrac141


frac14 prod

I

ifrac141



ΣG










p μ G

ΣGf g







obtained)












^ L frac14 argmaxL


asymp argmaxL

p L j^ x ^ μ G

ΣG

n o Y α xr

β K


^ x ^ μ G

ΣG


x μ Gf g ΣGf g

p x μ G

ΣGf gjY α xr

β K

eth7THORN



^ x ^ μ G

ΣG


x μ Gf g Σ Gf g

p Y jα x K μ G

ΣGf g

p xj β xr

Keth THORN p μ G

ΣGf g

frac14



XI

ifrac141 log


h ithorn

XG


eth8THORN








ΩGi frac14




XI

ifrac141ΩGi y i

ν G thornXI

ifrac141ΩG

i

ΣGlarr

XI

ifrac141ΩG


XI

ifrac141ΩG

i


ΣG



p L j^ x ^ μ G

ΣG

n o


li asymp argmaxk



V k frac14XI

ifrac141



Xk


pi k0jα x K

eth9THORN


hyperparameters































interpolation















































































































































































































































6


Table 4








LR average

(Yushkevich et al)


Parasubiculum 015 73 027 022 134 019

Presubiculum 021 121 020 008 41 040

Subiculum 014 66 029 018 95 023 25 057 59 027

CA1 003 24 058 002 18 069 11 095 10 (CA123) 099

CA23 002 18 071 010 47 036 27 (CA12) 055

CA4 003 23 059 004 25 057 26 (CA4DG) 042


Molec layer 002 20 067 005 28 052

Fimbria 002 19 068 004 26 055

Hippo 1047297ssure 045 N1000 010 026 187 017

HATA 020 111 021 007 36 043

Hippo tail 045 N1000 010 049 N1000 010

Whole hippo 004 27 054 004 25 056


Perirhinal 223 010

Table 5




Left T1 010 047 023 008 012 008 011 009 004 030 030 044 008

T1 + T2 015 021 014 003 002 003 002 002 002 045 020 045 004

Right T1 034 047 032 010 025 008 006 012 007 035 021 028 010

T1 + T2 022 008 018 002 010 004 001 005 004 026 007 049 004



















































































Table 6



the two groups





Subiculum 189 178 189 154

CA1 199 090 182 067

CA23 158 139 159 124

CA4 179 153 180



Fimbria 060 070 039 067


HATA 145 151

























































































Table 7


Atlas Accuracy

at elbow

AUROC


Whole hippocampus


840 0901
























































Acknowledgments





















Sub1047297

eld Volumetryrdquo














































XI

ifrac141ΩG

i ~ y i

ν G thornXI

ifrac141ΩG

i




o ieth THORNG


o ieth THORNG


ΣGlarr

XI

ifrac141ΩG


t thorn ~Ψi


XI

ifrac141

ΩG

i






i frac14 0 and ~Ψm


mo ieth THORNG Σ

o ieth THORNG

h iminus1

Σmo ieth THORNG




pi y ij μ GΣG

frac14 N y o

i μo ieth THORN


h i











References













































































































































Generative model























Table 3





Ex vivo atlas 786 51 254 337 520 179 211 244 465 466 50 92 320


UPenn NA 1574 86 201 167 127

Simica

802 404 591 139 197 59Harding 69 321 529 731 138 169 50










ifrac141


frac14 prod

I

ifrac141



ΣG










p μ G

ΣGf g







obtained)












^ L frac14 argmaxL


asymp argmaxL

p L j^ x ^ μ G

ΣG

n o Y α xr

β K


^ x ^ μ G

ΣG


x μ Gf g ΣGf g

p x μ G

ΣGf gjY α xr

β K

eth7THORN



^ x ^ μ G

ΣG


x μ Gf g Σ Gf g

p Y jα x K μ G

ΣGf g

p xj β xr

Keth THORN p μ G

ΣGf g

frac14



XI

ifrac141 log


h ithorn

XG


eth8THORN








ΩGi frac14




XI

ifrac141ΩGi y i

ν G thornXI

ifrac141ΩG

i

ΣGlarr

XI

ifrac141ΩG


XI

ifrac141ΩG

i


ΣG



p L j^ x ^ μ G

ΣG

n o


li asymp argmaxk



V k frac14XI

ifrac141



Xk


pi k0jα x K

eth9THORN


hyperparameters































interpolation















































































































































































































































6


Table 4








LR average

(Yushkevich et al)


Parasubiculum 015 73 027 022 134 019

Presubiculum 021 121 020 008 41 040

Subiculum 014 66 029 018 95 023 25 057 59 027

CA1 003 24 058 002 18 069 11 095 10 (CA123) 099

CA23 002 18 071 010 47 036 27 (CA12) 055

CA4 003 23 059 004 25 057 26 (CA4DG) 042


Molec layer 002 20 067 005 28 052

Fimbria 002 19 068 004 26 055

Hippo 1047297ssure 045 N1000 010 026 187 017

HATA 020 111 021 007 36 043

Hippo tail 045 N1000 010 049 N1000 010

Whole hippo 004 27 054 004 25 056


Perirhinal 223 010

Table 5




Left T1 010 047 023 008 012 008 011 009 004 030 030 044 008

T1 + T2 015 021 014 003 002 003 002 002 002 045 020 045 004

Right T1 034 047 032 010 025 008 006 012 007 035 021 028 010

T1 + T2 022 008 018 002 010 004 001 005 004 026 007 049 004



















































































Table 6



the two groups





Subiculum 189 178 189 154

CA1 199 090 182 067

CA23 158 139 159 124

CA4 179 153 180



Fimbria 060 070 039 067


HATA 145 151

























































































Table 7


Atlas Accuracy

at elbow

AUROC


Whole hippocampus


840 0901
























































Acknowledgments





















Sub1047297

eld Volumetryrdquo














































XI

ifrac141ΩG

i ~ y i

ν G thornXI

ifrac141ΩG

i




o ieth THORNG


o ieth THORNG


ΣGlarr

XI

ifrac141ΩG


t thorn ~Ψi


XI

ifrac141

ΩG

i






i frac14 0 and ~Ψm


mo ieth THORNG Σ

o ieth THORNG

h iminus1

Σmo ieth THORNG




pi y ij μ GΣG

frac14 N y o

i μo ieth THORN


h i











References































































































ifrac141


frac14 prod

I

ifrac141



ΣG










p μ G

ΣGf g







obtained)












^ L frac14 argmaxL


asymp argmaxL

p L j^ x ^ μ G

ΣG

n o Y α xr

β K


^ x ^ μ G

ΣG


x μ Gf g ΣGf g

p x μ G

ΣGf gjY α xr

β K

eth7THORN



^ x ^ μ G

ΣG


x μ Gf g Σ Gf g

p Y jα x K μ G

ΣGf g

p xj β xr

Keth THORN p μ G

ΣGf g

frac14



XI

ifrac141 log


h ithorn

XG


eth8THORN








ΩGi frac14




XI

ifrac141ΩGi y i

ν G thornXI

ifrac141ΩG

i

ΣGlarr

XI

ifrac141ΩG


XI

ifrac141ΩG

i


ΣG



p L j^ x ^ μ G

ΣG

n o


li asymp argmaxk



V k frac14XI

ifrac141



Xk


pi k0jα x K

eth9THORN


hyperparameters































interpolation















































































































































































































































6


Table 4








LR average

(Yushkevich et al)


Parasubiculum 015 73 027 022 134 019

Presubiculum 021 121 020 008 41 040

Subiculum 014 66 029 018 95 023 25 057 59 027

CA1 003 24 058 002 18 069 11 095 10 (CA123) 099

CA23 002 18 071 010 47 036 27 (CA12) 055

CA4 003 23 059 004 25 057 26 (CA4DG) 042


Molec layer 002 20 067 005 28 052

Fimbria 002 19 068 004 26 055

Hippo 1047297ssure 045 N1000 010 026 187 017

HATA 020 111 021 007 36 043

Hippo tail 045 N1000 010 049 N1000 010

Whole hippo 004 27 054 004 25 056


Perirhinal 223 010

Table 5




Left T1 010 047 023 008 012 008 011 009 004 030 030 044 008

T1 + T2 015 021 014 003 002 003 002 002 002 045 020 045 004

Right T1 034 047 032 010 025 008 006 012 007 035 021 028 010

T1 + T2 022 008 018 002 010 004 001 005 004 026 007 049 004



















































































Table 6



the two groups





Subiculum 189 178 189 154

CA1 199 090 182 067

CA23 158 139 159 124

CA4 179 153 180



Fimbria 060 070 039 067


HATA 145 151

























































































Table 7


Atlas Accuracy

at elbow

AUROC


Whole hippocampus


840 0901
























































Acknowledgments





















Sub1047297

eld Volumetryrdquo














































XI

ifrac141ΩG

i ~ y i

ν G thornXI

ifrac141ΩG

i




o ieth THORNG


o ieth THORNG


ΣGlarr

XI

ifrac141ΩG


t thorn ~Ψi


XI

ifrac141

ΩG

i






i frac14 0 and ~Ψm


mo ieth THORNG Σ

o ieth THORNG

h iminus1

Σmo ieth THORNG




pi y ij μ GΣG

frac14 N y o

i μo ieth THORN


h i











References






































































































































































































































































































































6


Table 4








LR average

(Yushkevich et al)


Parasubiculum 015 73 027 022 134 019

Presubiculum 021 121 020 008 41 040

Subiculum 014 66 029 018 95 023 25 057 59 027

CA1 003 24 058 002 18 069 11 095 10 (CA123) 099

CA23 002 18 071 010 47 036 27 (CA12) 055

CA4 003 23 059 004 25 057 26 (CA4DG) 042


Molec layer 002 20 067 005 28 052

Fimbria 002 19 068 004 26 055

Hippo 1047297ssure 045 N1000 010 026 187 017

HATA 020 111 021 007 36 043

Hippo tail 045 N1000 010 049 N1000 010

Whole hippo 004 27 054 004 25 056


Perirhinal 223 010

Table 5




Left T1 010 047 023 008 012 008 011 009 004 030 030 044 008

T1 + T2 015 021 014 003 002 003 002 002 002 045 020 045 004

Right T1 034 047 032 010 025 008 006 012 007 035 021 028 010

T1 + T2 022 008 018 002 010 004 001 005 004 026 007 049 004



















































































Table 6



the two groups





Subiculum 189 178 189 154

CA1 199 090 182 067

CA23 158 139 159 124

CA4 179 153 180



Fimbria 060 070 039 067


HATA 145 151

























































































Table 7


Atlas Accuracy

at elbow

AUROC


Whole hippocampus


840 0901
























































Acknowledgments





















Sub1047297

eld Volumetryrdquo














































XI

ifrac141ΩG

i ~ y i

ν G thornXI

ifrac141ΩG

i




o ieth THORNG


o ieth THORNG


ΣGlarr

XI

ifrac141ΩG


t thorn ~Ψi


XI

ifrac141

ΩG

i






i frac14 0 and ~Ψm


mo ieth THORNG Σ

o ieth THORNG

h iminus1

Σmo ieth THORNG




pi y ij μ GΣG

frac14 N y o

i μo ieth THORN


h i











References










































































































































































Table 6



the two groups





Subiculum 189 178 189 154

CA1 199 090 182 067

CA23 158 139 159 124

CA4 179 153 180



Fimbria 060 070 039 067


HATA 145 151

























































































Table 7


Atlas Accuracy

at elbow

AUROC


Whole hippocampus


840 0901
























































Acknowledgments





















Sub1047297

eld Volumetryrdquo














































XI

ifrac141ΩG

i ~ y i

ν G thornXI

ifrac141ΩG

i




o ieth THORNG


o ieth THORNG


ΣGlarr

XI

ifrac141ΩG


t thorn ~Ψi


XI

ifrac141

ΩG

i






i frac14 0 and ~Ψm


mo ieth THORNG Σ

o ieth THORNG

h iminus1

Σmo ieth THORNG




pi y ij μ GΣG

frac14 N y o

i μo ieth THORN


h i











References









































































































































































Table 7


Atlas Accuracy

at elbow

AUROC


Whole hippocampus


840 0901
























































Acknowledgments





















Sub1047297

eld Volumetryrdquo














































XI

ifrac141ΩG

i ~ y i

ν G thornXI

ifrac141ΩG

i




o ieth THORNG


o ieth THORNG


ΣGlarr

XI

ifrac141ΩG


t thorn ~Ψi


XI

ifrac141

ΩG

i






i frac14 0 and ~Ψm


mo ieth THORNG Σ

o ieth THORNG

h iminus1

Σmo ieth THORNG




pi y ij μ GΣG

frac14 N y o

i μo ieth THORN


h i











References













































































































































Acknowledgments





















Sub1047297

eld Volumetryrdquo














































XI

ifrac141ΩG

i ~ y i

ν G thornXI

ifrac141ΩG

i




o ieth THORNG


o ieth THORNG


ΣGlarr

XI

ifrac141ΩG


t thorn ~Ψi


XI

ifrac141

ΩG

i






i frac14 0 and ~Ψm


mo ieth THORNG Σ

o ieth THORNG

h iminus1

Σmo ieth THORNG




pi y ij μ GΣG

frac14 N y o

i μo ieth THORN


h i











References





























































































i frac14 0 and ~Ψm


mo ieth THORNG Σ

o ieth THORNG

h iminus1

Σmo ieth THORNG




pi y ij μ GΣG

frac14 N y o

i μo ieth THORN


h i











References

























































































a computational atlas of the hippocampal formation using ex vivo, ultra-high resolution mri-...

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